# Sequences converge or diverge?

## Homework Statement

I need to see if these sequences converge or diverge:

1) $$a_n = ncosn\pi$$

2) $${ 0,1,0,0,1,0,0,0,1,0,0,0,0,1,... }$$

3) $$a_n = \frac{1 . 3 . 5 . ... (2n - 1)}{n!}$$

## The Attempt at a Solution

1) $$]cosn\pi = -1[/itex] so [itex]a_n \to -\infty$$?

2) What is this. where is the n?

3) Not sure

## Answers and Replies

Matterwave
Gold Member
1) are you sure cos(n*pi)=-1 always? What's cos(0) or cos(2*pi)?

2) There is no n, it's a pattern sequence.

3) What convergence/divergence tests have you thought of applying to this? Have you gotten anywhere with it? The last course I took that involved proving convergence/divergence was 3 years ago...so I don't remember every test that could be applied.

Dick