Question about alternating series test...?

Question

n=0 Σ ∞ -1^(n+1)*e^n / 3^(n+1)


Determine whether series is convergent or divergent, and if convergent find its sum.

I think it's convergent due to alternating series test, but I can't figure out its sum...

Answer 1

Sum = (1/3)/[1+e/3], for a geometric series with r = -e/3.
Since the |r| = e/3 < 1, the series is convergent absolutely.

Answer 2

in abs.val (an+1)/an= e/3 ==> e/3<1 so it is absolutely convergent
Its a geometric series with r=(-e/3)
S=1/3 (1/(1+e/3))= 1/(3+e)