Series (p-series)

1. Dec 9, 2009

naspek

if my an = 1 / (n+1)^2
can i use p series test to confirm that the series will converge..
where p = 2..

2. Dec 9, 2009

Staff: Mentor

Sure. If your series is something like this,
$$\sum_{n = 0}^{\infty} \frac{1}{(n + 1)^2}$$

you can change the series index to write the series this way:
$$\sum_{n = 1}^{\infty} \frac{1}{n^2}$$

3. Dec 9, 2009

naspek

it's comparison test right?
the series will converge..
am i right?

4. Dec 9, 2009

VeeEight

p-series converge for p>1, so yes, your summation converges.

5. Dec 9, 2009

Staff: Mentor

You don't need the comparison test if you know the p-series test, and this is a p-series.

6. Dec 10, 2009

HallsofIvy

Staff Emeritus
I believe that naspek was saying that he can argue that $1/(n+1)^2< 1/n^2$ and so use the comparison test without using your idea of changing the index.