+47 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?
+33615 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 nth 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.
