Find the sum of the first n
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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
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
Answers (5)
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
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
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_reverse
sum_harm_forward - sum_harm_reverse
Roger Stafford
on 15 Feb 2017
Or how about this one-liner:
H = det(diag(2:n)+ones(n-1))/factorial(n);
2 Comments
Walter Roberson
on 8 Sep 2018
syms x n
symsum(1/x, x, 1, n)
1 Comment
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.
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
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)
double(subs(S, m, [10 100 500]))
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
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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