AT&T; LTE 11:09 AM 1 * 92% Solved: Find The Interval Of Convergence Of The P www

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AT&T; LTE 11:09 AM 1 * 92% Solved: Find The Interval Of Convergence Of The P www.chegg.com and answers/ find the interval of convergence of the Question: Find the interval of... ind the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval. If the interval of convergence is an interval, enter your answer using interval notation. If the interval of convergence is a finite set, enter your answer using set notation infinity ? (2n)(z/2)" n-0 Expert Answer ? b100% (1 rating) VIEW THIS ANSWER

Explanation / Answer

an = (2n)! * (x/2)^n

a(n+1) = (2n+2)! * (x/2)^(n+1)

Now, find ratio a(n+1)/a(n), we get :

(2n+2)! * (x/2)^(n+1)
divided by
(2n)! * (x/2)^n

Cancel stuff out :
(2n+2)(2n+1) * (x/2)

Now, find lim n ---> inf,
clearly (2n+2)*(2n+1) will result in inf

So, the limit n--->inf (a(n+1)/a(n)) = inf
which is > 1

So, by ratio test, this series
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