calculus question?

Question

Find the values of "x" for which the series converges. Find the sum of the series for those values of "x".

1) summation notation symbol (with n=1 on bottom and infinity on top) of x^n/3^n

2) summation notation symbol (with n=0 on bottom and infinity on top) of cos^nx/2^n

show steps so i know how u did it..thanks

Answer 1

1) = (x/3)^n geometric series r= x/3 convergent if I x/3 I <1
for these values the sum is 1/[1-x/3]
2)In abs val c< 1/2raised n geometric series absolutely convergent.I don´t know the sum and think no one knows exactly