For what values of p will both series(

Question

#7 For what values of p will both series( 1 is the lower limit ; ∞ is the upper limit ; function is (1)/(n^(2p)) and (1 is the lower limit; ; ∞ is the upper limit ; function is (p/2)^n converges?)

1. -2<p<2 only
2. -½<p<½ only
3. ½<p<2 only
4. p<½ and p>2 
5. There are no such values of p

Answer 1

First series converges if 2p > 1 or p > 1/2 (p-series)

Second series converges if Ip/2I < 1 or - 2 < p < 2 (geometric series)

So, for 1/2 < p < 2 only both series converges