Write a MATLAB function to approximate the infinite series ∑n=1^∞ (1)/(n(n+5)) using N terms,. T

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Question

Write a MATLAB function to approximate the infinite series \sum_{n=1}^{\infty} \frac{1}{n(n+5)} using N terms,. The value of N is the input of the function and the function should return the approximation of the series \sum_{n=1}^{\infty} \frac{1}{n(n+5)} for the N terms and how close the approximation is to the limit of the series. This series is a telescoping series [1] and the limit of the series of this type as N approaches infinity is \lim_{N \to \infty} \sum_{n=1}^{N} \frac{1}{n(n+k)} = \frac{H_k}{k}, where $H_k$ is the kth harmonic number [2]. For this problem, k = 5 and the series limit to four decimal places is 0.4567. Your function should compute the approximation using recursion: 1. Using a revursive function to implement the function. Do not use element by element operations or MATLAB's sum function. 2. Calculate and return the the percent errors between your approximations and the limit of the series (0.4567 for k=5). Subtract the limit from your calculated approximation and divide the result by the limit and multiply it with 100 3. Test your program for N = 1, N = 10, and N = 100 on your own MATLAB installation. Function 1 function [approx, errPercent] =sumOfTelescoping(N) 2 limit=0.4567; 3 % implement it using recursion, no loop, no sum() 4 5 6 7 8 end

          Write a MATLAB function to approximate the infinite series \sum_{n=1}^{\infty} \frac{1}{n(n+5)} using N terms,. The value of N is the input of the function and the function should return the approximation of the series \sum_{n=1}^{\infty} \frac{1}{n(n+5)} for the N terms and how close the approximation is to the limit of the series. This series is a telescoping series [1] and the limit of the series of this type as N approaches infinity is \lim_{N \to \infty} \sum_{n=1}^{N} \frac{1}{n(n+k)} = \frac{H_k}{k}, where $H_k$ is the kth harmonic number [2]. For this problem, k = 5 and the series limit to four decimal places is 0.4567.

Your function should compute the approximation using recursion:
1. Using a revursive function to implement the function. Do not use element by element operations or MATLAB's sum function.
2. Calculate and return the the percent errors between your approximations and the limit of the series (0.4567 for k=5). Subtract the limit from your calculated approximation and divide the result by the limit and multiply it with 100
3. Test your program for N = 1, N = 10, and N = 100 on your own MATLAB installation.
Function
1 function [approx, errPercent] =sumOfTelescoping(N)
2     limit=0.4567;
3     % implement it using recursion, no loop, no sum()
4 
5 
6 
7 
8 
end

Write a MATLAB function to approximate the infinite series ∑n=1^∞ (1)/(n(n+5)) using N terms,. The value of N is the input of the function and the function should return the approximation of the series ∑n=1^∞ (1)/(n(n+5)) for the N terms and how close the approximation is to the limit of the series. This series is a telescoping series [1] and the limit of the series of this type as N approaches infinity is limN →∞ ∑n=1^N (1)/(n(n+k)) = (Hk)/(k), where Hk is the kth harmonic number [2]. For this problem, k = 5 and the series limit to four decimal places is 0.4567.

Your function should compute the approximation using recursion:
1. Using a revursive function to implement the function. Do not use element by element operations or MATLAB's sum function.
2. Calculate and return the the percent errors between your approximations and the limit of the series (0.4567 for k=5). Subtract the limit from your calculated approximation and divide the result by the limit and multiply it with 100
3. Test your program for N = 1, N = 10, and N = 100 on your own MATLAB installation.
Function
1 function [approx, errPercent] =sumOfTelescoping(N)
2 limit=0.4567;
3 % implement it using recursion, no loop, no sum()
4
5
6
7
8
end

Added by Jason B.

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