Write a user defined function psum.m to approximate the value of the sum K2 1223

Question

Write a user defined function psum.m to approximate the value of the sum K2 12232 by adding terms to the sum until the difference (error) between the sum and/6 is smaller than a given tolerance tol. The function input is tol, and its outputs are the sum, the number of steps that it took to obtain it, and the error. Therefore the first line of the function m-file should read as: function [sum, steps,error-psum (tol). Note: psum must contain a while-loop; prior to the loop it will require an initial "partial sum", the actual "answer", and an initial error (magnitude of difference between answer and partial sum) to initialize the loop (a) Call your function psum from Project 2.m with each of five tolerance values 10.1, 0.05, 0.01, 0.005, 0.001. Save the error corresponding to each tolerance in a vector called errors, and the number of steps for each tolerance in a vector called total-Steps. This can be done by o with 5 iterations that inputs a new tolerance into psum each calling psum within a for-loop time, OR you may repeat the call to psum 5 times separately

Explanation / Answer

function dummy=project2()
clc;
clear all;
tol=[0.1 0.05 0.01 0.005 0.001];
for i=1:5
disp('__________________')
tolernece =tol(i)
disp('__________________')
[sum,steps,error]=psm(tol(i))

end

function [sum,steps,error]=psm(tol)
sum=0;
k=1;
steps=0;
error=1;
while(error>tol)
sum=sum+1/k^2;
k=k+1;
error=abs(sum-pi^2/6);
steps=steps+1;
end
  
end
end

%%% Solution %%%

__________________

tolernece =

0.1000

__________________

sum =

1.5498

steps =

10

error =

0.0952

__________________

tolernece =

0.0500

__________________

sum =

1.5962

steps =

20

error =

0.0488

__________________

tolernece =

0.0100

__________________

sum =

1.6350

steps =

100

error =

0.0100

__________________

tolernece =

0.0050

__________________

sum =

1.6399

steps =

200

error =

0.0050

__________________

tolernece =

1.0000e-03

__________________

sum =

1.6439

steps =

1000

error =

9.9950e-04

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