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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?

 Jan 27, 2020
 #1
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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.

 Jan 27, 2020

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