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Find the sum of the first n

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bassam792
bassam792 on 15 Feb 2017
Commented: Steven Lord on 14 Feb 2024
Find the sum of the first n terms of the harmonic series where n is an integer greater than one 1+1/2+1/3+1/4+1/5+.....
  1 Comment
Yogesh
Yogesh on 14 Feb 2024
Consider the following divergent infinite series:
S=1/2+2/3+3/4+⋯+n/n+1
Write a MATLAB code that takes a value of n and returns S.
Please report the values below: Please report the value of S for n=10

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Answers (5)

John Chilleri
John Chilleri on 15 Feb 2017
Edited: John Chilleri on 15 Feb 2017
Hello,
This can be done simply with,
n = 100; % whatever you want
sum_harm = 0;
for i = 1:n
sum_harm = sum_harm + 1/i;
end
or even,
n = 100; % whatever you want
sum_harm = sum(1./(1:n));
Hope this helps!
  7 Comments
Walter Roberson
Walter Roberson on 8 Sep 2018
The theoretical sum would be the same. If you are using floating point then the result could differ. The order of operations of built-in functions like harmonic() is not specified. For doing it yourself, replace 1:n by n:-1:1
Walter Roberson
Walter Roberson on 4 Jun 2021
format long g
n = 1e10; % whatever you want
sum_harm_forward = 0;
sum_harm_reverse = 0;
for i = 1:n
sum_harm_forward = sum_harm_forward + 1/i;
sum_harm_reverse = sum_harm_reverse + 1/(n - i + 1);
end
sum_harm_forward
sum_harm_forward =
23.6030665949975
sum_harm_reverse
sum_harm_reverse =
23.6030665948883
sum_harm_forward - sum_harm_reverse
ans =
1.092317347684e-10

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Roger Stafford
Roger Stafford on 15 Feb 2017
Or how about this one-liner:
H = det(diag(2:n)+ones(n-1))/factorial(n);
  2 Comments
Ahmad Taheri
Ahmad Taheri on 26 Dec 2020
hi ,admin
one qustions
∑1/n=?
∑1/n^2=??
Walter Roberson
Walter Roberson on 26 Dec 2020
∑1/n is infinite.
∑1/n^2 is pi^2/6

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Walter Roberson
Walter Roberson on 8 Sep 2018
syms x n
symsum(1/x, x, 1, n)
  1 Comment
Hesbon Osoro
Hesbon Osoro on 3 Jun 2021
Very much useful to test the convergence of a harmonic series without lagging a machine, so fast code also. It is of great help.

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Vaibhav
Vaibhav on 15 Feb 2023
the examples in the course videos have been about convergent series. In this example, you will code a series that does not converge: S=1+12√+13√+⋯+1n√
Write a MATLAB code that takes a value of n and returns S. Please report the values below:
Please report the value of S for n=10
Please report the value of S for n=100
Please report the value of S for n=500
  1 Comment
Walter Roberson
Walter Roberson on 15 Feb 2023
Is that the sum of 1 + 1*x^(1/2) + 1*x^(1/3) ... + 1*x^(1/n) ?
Is it the sum of 1 + 1/sqrt(2) + 1/sqrt(3) + ... + 1/sqrt(n) ?
format long g
syms n m
S = 1 + symsum(1/sqrt(factorial(n)), n, 2, m)
S = 
double(subs(S, m, [10 100 500]))
ans = 1×3
2.46928512326805 2.46950631452105 2.46950631452105

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Yogesh
Yogesh on 14 Feb 2024
Consider the following divergent infinite series:
S=1/2+2/3+3/4+⋯+n/n+1
Write a MATLAB code that takes a value of n and returns S.
Please report the values below: Please report the value of S for n=10
  1 Comment
Steven Lord
Steven Lord on 14 Feb 2024
This sounds like a homework assignment. If it is, show us the code you've written to try to solve the problem and ask a specific question about where you're having difficulty and we may be able to provide some guidance.
If you aren't sure where to start because you're not familiar with how to write MATLAB code, I suggest you start with the free MATLAB Onramp tutorial to quickly learn the essentials of MATLAB.
If you aren't sure where to start because you're not familiar with the mathematics you'll need to solve the problem, I recommend asking your professor and/or teaching assistant for help.

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