# Find the positive values of p for which the series converges. (Enter your answer using interval notation.) ?

Find the positive values of p for which the series converges. (Enter your answer using interval notation.)

### 2 Answers

- AlvinLv 44 months ago
Since your question ask from the positive value ,

p> 1 which is

(1, + infinity) in interval notation is correct final answer.

but other statements in the your 1st answer are incorrect

-1 < (1/p) < 1

if p is negative

(1/p) > (-1)

multiply both sides by -p (which is positive )

-1 > p

so the total answer without your positive restriction

is

p< -1 or p> 1

without your positive restriction

(-infinity, -1) U ( 1, +infinity)

but your answer ask for only positive answers

so

(1, + infinity)

- 4 months ago
1/p^n is the same as (1/p)^n

For an infinite geometric sum, r^n converges when -1 < r < 1

-1 < 1/p < 1

-1 < 1/p

-1/p < 1

-1 < p

1/p < 1

1 < p

p > -1 and p > 1. The common set is p > 1. When p > 1, then the series converges.