Problem 46828. Approximate functions 2 (★★★★)

Created by Anirban Pal

Solve Later

{"parts":[{"partUri":"/matlab/document.xml","contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?><w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Compute the following sum for any given x and number of terms n.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"center\"/></w:pPr><w:customXml w:element=\"image\"><w:customXmlPr><w:attr w:name=\"height\" w:val=\"41\"/><w:attr w:name=\"width\" w:val=\"368\"/><w:attr w:name=\"verticalAlign\" w:val=\"baseline\"/><w:attr w:name=\"altText\" w:val=\"\"/><w:attr w:name=\"relationshipId\" w:val=\"rId1\"/></w:customXmlPr></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Here m! denotes the factorial of m, which the product of all natural numbers upto m, for example</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[2! = 1x2 = 2\n3! = 1x2x3 = 6\n5! = 1x2x3x4x5 = 120]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>If x=1 and n = 4, we have</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:customXml w:element=\"image\"><w:customXmlPr><w:attr w:name=\"height\" w:val=\"-1\"/><w:attr w:name=\"width\" w:val=\"-1\"/><w:attr w:name=\"verticalAlign\" w:val=\"baseline\"/><w:attr w:name=\"altText\" w:val=\"\"/><w:attr w:name=\"relationshipId\" w:val=\"rId2\"/></w:customXmlPr></w:customXml></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/><w:jc w:val=\"left\"/></w:pPr><w:r><w:t>Avoid using for/while loops.</w:t></w:r></w:p></w:body></w:document>","relationship":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/image","target":"/media/image1.gif","relationshipId":"rId1"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/image","target":"/media/image2.gif","relationshipId":"rId2"}]},{"partUri":"/media/image1.gif","contentType":"image/gif","content":"data:image/gif;base64,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","relationship":null},{"partUri":"/media/image2.gif","contentType":"image/gif","content":"data:image/gif;base64,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","relationship":null}],"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","target":"/matlab/document.xml","relationshipId":"rId1"}]}

<div style = "text-align: start; line-height: 20.4333px; min-height: 0px; white-space: normal; color: rgb(0, 0, 0); font-family: Menlo, Monaco, Consolas, monospace; font-style: normal; font-size: 14px; font-weight: 400; text-decoration: rgb(0, 0, 0); white-space: normal; "><div style="block-size: 291.3px; display: block; min-width: 0px; padding-block-start: 0px; padding-top: 0px; perspective-origin: 407px 145.65px; transform-origin: 407px 145.65px; vertical-align: baseline; "><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 205.533px 10.5px; transform-origin: 205.533px 10.5px; unicode-bidi: normal; "><span style="">Compute the following sum for any given x and number of terms n.</span></span></div><div style="block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: center; transform-origin: 384px 22.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><img class="imageNode" style="vertical-align: baseline" src="data:image/gif;base64,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" data-image-state="image-loaded"></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 296.392px 10.5px; transform-origin: 296.392px 10.5px; unicode-bidi: normal; "><span style="">Here m! denotes the factorial of m, which the product of all natural numbers upto m, for example</span></span></div><div style="background-color: rgb(247, 247, 247); block-size: 61.3px; border-bottom-left-radius: 4px; border-bottom-right-radius: 4px; border-end-end-radius: 4px; border-end-start-radius: 4px; border-start-end-radius: 4px; border-start-start-radius: 4px; border-top-left-radius: 4px; border-top-right-radius: 4px; margin-block-end: 10px; margin-block-start: 10px; margin-bottom: 10px; margin-inline-end: 3px; margin-inline-start: 3px; margin-left: 3px; margin-right: 3px; margin-top: 10px; perspective-origin: 404px 30.65px; transform-origin: 404px 30.65px; margin-left: 3px; margin-top: 10px; margin-bottom: 10px; margin-right: 3px; "><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 50.6px 8.5px; transform-origin: 50.6px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; perspective-origin: 4.21667px 8.5px; transform-origin: 4.21667px 8.5px; ">2</span><span style="border-block-end-color: rgb(178, 140, 0); border-block-start-color: rgb(178, 140, 0); border-bottom-color: rgb(178, 140, 0); border-inline-end-color: rgb(178, 140, 0); border-inline-start-color: rgb(178, 140, 0); border-left-color: rgb(178, 140, 0); border-right-color: rgb(178, 140, 0); border-top-color: rgb(178, 140, 0); caret-color: rgb(178, 140, 0); color: rgb(178, 140, 0); column-rule-color: rgb(178, 140, 0); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(178, 140, 0); perspective-origin: 46.3833px 8.5px; text-decoration: none; text-decoration-color: rgb(178, 140, 0); text-emphasis-color: rgb(178, 140, 0); transform-origin: 46.3833px 8.5px; ">! = 1x2 = 2</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 59.0333px 8.5px; transform-origin: 59.0333px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; perspective-origin: 4.21667px 8.5px; transform-origin: 4.21667px 8.5px; ">3</span><span style="border-block-end-color: rgb(178, 140, 0); border-block-start-color: rgb(178, 140, 0); border-bottom-color: rgb(178, 140, 0); border-inline-end-color: rgb(178, 140, 0); border-inline-start-color: rgb(178, 140, 0); border-left-color: rgb(178, 140, 0); border-right-color: rgb(178, 140, 0); border-top-color: rgb(178, 140, 0); caret-color: rgb(178, 140, 0); color: rgb(178, 140, 0); column-rule-color: rgb(178, 140, 0); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(178, 140, 0); perspective-origin: 54.8167px 8.5px; text-decoration: none; text-decoration-color: rgb(178, 140, 0); text-emphasis-color: rgb(178, 140, 0); transform-origin: 54.8167px 8.5px; ">! = 1x2x3 = 6</span></span></div><div style="background-color: rgba(0, 0, 0, 0); block-size: 20.4333px; border-bottom-left-radius: 0px; border-bottom-right-radius: 0px; border-end-end-radius: 0px; border-end-start-radius: 0px; border-inline-end-color: rgb(233, 233, 233); border-inline-end-style: solid; border-inline-end-width: 1px; border-inline-start-color: rgb(233, 233, 233); border-inline-start-style: solid; border-inline-start-width: 1px; border-left-color: rgb(233, 233, 233); border-left-style: solid; border-left-width: 1px; border-right-color: rgb(233, 233, 233); border-right-style: solid; border-right-width: 1px; border-start-end-radius: 0px; border-start-start-radius: 0px; border-top-left-radius: 0px; border-top-right-radius: 0px; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; min-block-size: 18px; min-height: 18px; padding-inline-start: 4px; padding-left: 4px; perspective-origin: 404px 10.2167px; transform-origin: 404px 10.2167px; white-space: nowrap; "><span style="block-size: auto; border-inline-end-color: rgb(0, 0, 0); border-inline-end-style: none; border-inline-end-width: 0px; border-inline-start-color: rgb(0, 0, 0); border-inline-start-style: none; border-inline-start-width: 0px; border-left-color: rgb(0, 0, 0); border-left-style: none; border-left-width: 0px; border-right-color: rgb(0, 0, 0); border-right-style: none; border-right-width: 0px; display: inline; margin-inline-end: 45px; margin-right: 45px; min-block-size: 0px; min-height: 0px; padding-inline-start: 0px; padding-left: 0px; perspective-origin: 84.3333px 8.5px; transform-origin: 84.3333px 8.5px; unicode-bidi: normal; white-space: pre; margin-right: 45px; "><span style="margin-inline-end: 0px; margin-right: 0px; perspective-origin: 4.21667px 8.5px; transform-origin: 4.21667px 8.5px; ">5</span><span style="border-block-end-color: rgb(178, 140, 0); border-block-start-color: rgb(178, 140, 0); border-bottom-color: rgb(178, 140, 0); border-inline-end-color: rgb(178, 140, 0); border-inline-start-color: rgb(178, 140, 0); border-left-color: rgb(178, 140, 0); border-right-color: rgb(178, 140, 0); border-top-color: rgb(178, 140, 0); caret-color: rgb(178, 140, 0); color: rgb(178, 140, 0); column-rule-color: rgb(178, 140, 0); margin-inline-end: 0px; margin-right: 0px; outline-color: rgb(178, 140, 0); perspective-origin: 80.1167px 8.5px; text-decoration: none; text-decoration-color: rgb(178, 140, 0); text-emphasis-color: rgb(178, 140, 0); transform-origin: 80.1167px 8.5px; ">! = 1x2x3x4x5 = 120</span></span></div></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 10px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 10px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 10px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 78.3px 10.5px; transform-origin: 78.3px 10.5px; unicode-bidi: normal; "><span style="">If x=1 and n = 4, we have</span></span></div><div style="block-size: 45px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 22.5px; text-align: left; transform-origin: 384px 22.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><img class="imageNode" style="vertical-align: baseline" src="data:image/gif;base64,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" data-image-state="image-loaded"></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 84.4167px 10.5px; transform-origin: 84.4167px 10.5px; unicode-bidi: normal; "><span style="">Avoid using for/while loops.</span></span></div></div></div>

Solve

Solution Stats

73 Solutions
21 Solvers

Last Solution submitted on Dec 08, 2021

Last 200 Solutions

Problem Comments

Problem Recent Solvers21

Problem Tags

series sum sine approx

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 46828. Approximate functions 2 (★★★★)

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers21

Suggested Problems

More from this Author52

Problem Tags

Community Treasure Hunt

Problem 46828. Approximate functions 2 (★★★★)

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers21

Suggested Problems

More from this Author52

Problem Tags

Community Treasure Hunt

Players