series question again..?

Question

please take a look at the screenshot..
http://www.xy-plaza.com/kevin/math/series.jpg

it's from a previous year final.
but there's no answer to it..
please teach me how to do it please.
thanks.

Answer 1

Let`´s take absolute value
a_n=Ix+2I^n/[(n+1)*e^n]and apply the ratio test

a_n+1 /a_n= Ix+2I (n+1)/(n+2) *1/e with
lim=1/e*Ix+2I
If 1/eIx+2I<1 Ix+2I and -2-e if x<-2-e and x>-2+e lim a_n is NOT zero
so the series is divergent
At x=-2+e
Theseries is (-1)^n * 1/(n+1) which we know is conditionally convergent
and atx=-2-e the series becomes 1/(n+1) which is divergent