1. Consider the infinite series defined by. Infinity/the sume of/ n=1 (2n!/2^2n) *

What is the value of r from the ratio test?

What does this r value tell you about the series?

Vanessadeirdre Jan 27, 2020

#1**+2 **

This was answered here: https://web2.0calc.com/questions/consider-the-infinite-series-defined-by_2

However, the answerer didn't give the ratio r, so:

r is obtained by dividing the (n+1)^{th} term by the n^{th} term. If it gets to be greater than 1 then the series diverges. If it's less than 1 the series converges.

\(r=\frac{2(n+1)!2^{2n}}{2n!(2^{2(n+1)})}\)

so \(r=\frac{n+1}{2^2}\text{ hence }r>1\) for all n greater than 3.

Alan Jan 27, 2020