# Convergence or divergence (series)

1. May 13, 2012

### bfusco

1. The problem statement, all variables and given/known data
Ʃ[(-1)^n (cosn)^2]/√n

3. The attempt at a solution
i dont have the slightest clue where to start

2. May 13, 2012

### sharks

Since this is a series and there is an alternating sign in the consecutive partial sums, you should use the Alternating Series Test.
$$\sum^{\infty}_{n=?}(-1)^n \frac{(\cos n)^2}{√n}$$
You have not stated the initial value for n.

The first step: Let $a_n=\frac{(\cos n)^2}{√n}$. Find the limit and test if it's zero.
Second step: Is $a_{n+1}\leq a_n$?
If both of these conditions are satisfied, then the series converges.

Last edited: May 13, 2012
3. May 13, 2012

### JG89

The initial value for n doesn't matter. It's presumably not zero.

4. May 13, 2012

### sharks

The initial value of n is normally ignored, but stating the latter forms part of the proper notation when writing the series with the summation symbol.