Use the series Sigman 012 2k 1 k2 2k 1 To estimate the va

Use the series Sigma_n = 0^12 2^k + 1 (k!)^2/ (2k + 1)! To estimate the value of pi. To how many decimal places is this accurate? This series dates back to the work of Sir Isaac Newton (1642-1727). After 30 terms this series is accurate to 10 decimal places.

Solution

Using matlab we get the summation is:

3.14147964896...

pi=3.14159265359

So the summation is accurate to first 3 decimal places.