# Homework Help: How do you find out where a series converges

1. Mar 6, 2005

### stunner5000pt

are there certain formulae to find out where a certain infinite series converges, if it does converge

for example
$$\sum_{n=1}^\infty (\frac{3}{5})^n$$ certainly converges because it is between the infinite series
$$\sum (1+ \frac{1}{n})^n$$ and the series $$\sum (\frac{1}{5})^n$$ wich both converge Since both of them converge then sum(3/5)^n must converge.

But my question is WHERE does (3/5)^n converge??

Last edited: Mar 6, 2005
2. Mar 6, 2005

### Hurkyl

Staff Emeritus
$\sum_{n=1}^\infty (3/5)^n$ doesn't have any parameters, so it doesn't really make sense to ask for which values of the parameters (i.e. where) the series converges... only if.

Now, (1 + 1/n)^n and (1/5)^n aren't series...

Last edited: Mar 6, 2005
3. Mar 6, 2005

### stunner5000pt

what i meant was how do you find the explicit value of the series
for example i know (because ive been told) that
$$\sum \frac{1}{n^2} = \frac{\pi^2}{6}$$
would it be possible to that to do this series??

note: my proof of its convergence is wrong

4. Mar 6, 2005

### Hurkyl

Staff Emeritus
$\sum_{n = 1}^{\infty} (1 + 1/n)^n$ doesn't converge...

Anyways, yes, your series does have a sum. It's a geometric series, so use the formula for such series.

5. Mar 6, 2005