Find the sum of the first n

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bassam792
bassam792 2017-2-15
评论： Steven Lord 2024-2-14
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 个评论
Yogesh
Yogesh 2024-2-14
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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回答（5 个）

John Chilleri
John Chilleri 2017-2-15
编辑：John Chilleri 2017-2-15
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!
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显示 5更早的评论
Walter Roberson
Walter Roberson 2018-9-8
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 2021-6-4
Ran in:
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 2017-2-15
Or how about this one-liner:
H = det(diag(2:n)+ones(n-1))/factorial(n);
inspire by http://oeis.org/A000254.
  2 个评论
Ahmad Taheri
Ahmad Taheri 2020-12-26
hi ,admin
one qustions
∑1/n=?
∑1/n^2=??
Walter Roberson
Walter Roberson 2020-12-26
∑1/n is infinite.
∑1/n^2 is pi^2/6

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Walter Roberson
Walter Roberson 2018-9-8
syms x n
symsum(1/x, x, 1, n)
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Hesbon Osoro
Hesbon Osoro 2021-6-3
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 2023-2-15
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 个评论
Walter Roberson
Walter Roberson 2023-2-15
Ran in:
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 2024-2-14
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 个评论
Steven Lord
Steven Lord 2024-2-14
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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