# what values of p make this serries convergent

• Jul 31st 2009, 12:24 PM
superdude
what values of p make this serries convergent
Question:what does p need to be for this to be convergent
sum from 1 to infinity of $\frac{(-1)^{n-1}}{n^{p}}$
Confusion: I thought it would have to be p>1 like the "p-series" ( $\frac{1}{n^{p}}$ is convergent for p>1)
• Jul 31st 2009, 12:41 PM
skeeter
Quote:

Originally Posted by superdude
Question:what does p need to be for this to be convergent
sum from 1 to infinity of $\frac{(-1)^{n-1}}{n^{p}}$
Confusion: I thought it would have to be p>1 like the "p-series" ( $\frac{1}{n^{p}}$ is convergent for p>1)

p > 0 forms an alternating series whose nth term approaches 0 ... convergent.

http://www.mathwords.com/a/alternating_series_test.htm