hi guys I was asked to find the radius of convergence of the

hi guys, I was asked to find the radius of convergence of the series (n^n / n!) (x^n) (n=1 to and n goes to infinity). I used the ratio test for this problem but did something very wrong and ended up with lim n-> infinity n+1 which is not convergent at all. Would anyone please be kind enough to show me the steps on how to solve this problem, thank you very much in advance, I really appreciate your taking the time to help me out!

RAtio test

dont use ration test as their power is n so use root test :

lim n-> infintiy (Tn)^1/n

: n/ (n!)^1/n * x : lim turns out 0

: | Radius * 0 | = 1

radius of convergence : infinity !!!

hi guys, I was asked to find the radius of convergence of the series (n^n / n!) (x^n) (n=1 to and n goes to infinity). I used the ratio test for this problem bu

hi guys I was asked to find the radius of convergence of the

Solution

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