For the following power series: ∑ (4^n x^n)/([log(n+1)]^(n)

[Simkate]

For the following power series, find

∑ (4^n x^n)/([log(n+1)]^(n)

(a) the radius of convergence
(b) the interval of convergence, discussing the endpoint convergence when
the radius of convergence is finite.
-------------------------------------------------------------------------------

I wanted to know whether my solution is write, is it possible for somone to check it for me. Thank You

Due to the n-th powers, we use the root test.

r = lim(n-->∞) |4^n x^n / [log(n+1)]^n|^(1/n)
= lim(n-->∞) 4|x| / log(n+1)
= 0 for all x.

a) radius of convg= 0
b) interval of convg=0

since the series is infinte

 

[LCKurtz]

Are you sure you have read what the root test tells you correctly?