houw can I get the number of terms?

Write a program to compute the sum of the series :

2^3 +4^3 + 6^3 + ...

such that the sum is as large as possible without exceeding 1000. The program should display the sum and how many terms are used in the sum.

First, please don’t use the inbuilt function SUM.

Then, after getting the number of terms, please solve this problem using vectorisation.

[欣婷]

I misspelled the question.I want to ask how can I get the number of terms.

Answer 1

[Voss]

You can use a while loop:

total = 0;
ii = 0;

while total <= 1000
    ii = ii + 1;               % number of terms used so far
    total = total + something; % sum so far
end

disp(sprintf('The sum is %d',total));
disp(sprintf('The number of terms used is %d',ii));

You have to figure out what expression goes in place of "something".

Answer 2

[Walter Roberson]

First realize that the sum of 2 cube + 4 cube + 6 cube and so on, is 2 cube times (1 cube + 2 cube + 3 cube +...)

Now look up the formula for the sum of cubes of the first n natural numbers

https://www.cuemath.com/algebra/sum-of-cubes-of-n-natural-numbers/

and multiply it by 2 cube.

You now have a closed formula, and you have a target of 1000, and you can solve the equation. Then round down to the nearest integer.

[Walter Roberson]

I tested this method and it appears to work fine.

hint:

syms N positive

will avoid irrelevant roots of the equation.