It is possible to obtain the value of through the infinite sum In this problem, you

It is possible to obtain the value of π through the infinite sum

In this problem, you will explore the convergence of this summation for a finite number of terms N,

Write a MATLAB function that computes the value of this sum up to a desired value of the residual

The latter expression is only valid for N > 1. Your program should compute the value of π(N) and the number of terms N required to reach the first term where the residual is less than ϵ = 10⁻¹, 10⁻², . . . , 10⁻⁸. Make one semilog plot of the eight outputs for the value of the sum versus ϵ and a log–log plot of the eight outputs for the number of terms needed to compute the sum for a given value of ϵ. Your program should also output the value of π(N) and the value of N for ϵ = 10−8.

Transcribed Image Text:

π = Σ k=1 (-1)*+1 0.5k – 0.25΄