# Homework Help: Alternating series help

1. Jan 22, 2008

### rcmango

1. The problem statement, all variables and given/known data

Determine wheter the series is convergent or divergent. If it convergent, approximate the sum of the series correct to four decimal places.

heres the equation: http://img251.imageshack.us/img251/2261/46755781zg9.png [Broken]

2. Relevant equations

3. The attempt at a solution

This appears to be an alternating geometric series,

Would it be okay to move the exponent k over everything? in other words: ( (-1)/k) )^k

So then it looks alot like a geometric series, so then It converges by the rules of an alernating series, it is decreasing and it is approaching zero.

So then to find its sum, i would do so by geometric series right?

first term would be starting at k = 2, so: 1/2?

then use 1/2 divided by 1 -r

Am i on the right track? what is r??? is it also, 1/2?

Last edited by a moderator: May 3, 2017
2. Jan 22, 2008

### Pyrrhus

Yes you can use k as the exponent of the whole because of the distributive property of exponentiation.

3. Jan 22, 2008

### rcmango

how about the rest of what i'm doing here, this was my best hypothesis to approach the problem. I need help with the common ratio. i'm not sure what to use if its k^k ?

4. Jan 22, 2008

### dynamicsolo

It isn't a geometric series because such series has a constant ratio between successive terms. However, that gives you a clue to the proof of its convergence. (Try a comparison test.) As for the estimate of the sum, do they want an analytical proof of some sort or just something carried out on a calculator (how many terms do you need to get to a precision of 10^-4 ?)

Last edited by a moderator: May 3, 2017