Question

Create a Function file using Matlab.

function sums = estimSum (nTerms) Before we go much further, save your file and name it the exact name of the function, estimSum Inside the function file just created, write the code needed to compute partial sums 1)k+1 2k 1 k-1 and compare the output in each case to the value of by computing the remainder Rn- _Snl for each n - 20,50, 100, 1000. When calling the function in Matlab's command window for varying values of nTerms (n = 20, 50, 100, 1000) use (for example) sumS20 estimSum (20) Make a table (by hand) listing nTerms, the corresponding value of the sum Sn, along with the corresponding (exact) remainder Rn, as well as the next term in the sequence that was not included in the sum, an+il. How does Rn compare to lant for all the different n values tested (write this conclusion in a sentence)?

Answer 1

MATLAB CODE:

function sumS = estimSum(n)
    syms k
    f    = ((-1)^(k+1))/(2*k - 1);
    sumS = symsum(f,k,1,n);
    fprintf('Sum of %d terms,Sum = %0.3f\n',n,sumS)
    Remainder = abs((pi/4)-sumS);
    fprintf('Remainder = %0.3f',Remainder)
end

OUTPUT:

sumS20-estimSum (20) Sum of 20 terms,Sum0.773 Remainder - 0.012 sumS20- 129049485078524/166966608033225