Re: series converge

On Sep 4, 2005 4:39 AM, tamiry wrote:

> HW question I failed solving, please help
>
> does this converge?
>
>
> ( 3+(-1)^n)^n
> (sigma 1 to infinity)-------------
> n * 4^n
>

Rewrite your general term as

1/n * [(3 + (-1)^n)/4]^n.

Now let a_n = [(3 + (-1)^n)/4]^n, so you have

a_n = {1/2, 1, 1/2^3, 1, 1/2^5,...}.

Split your original sum up into two sums, one over the odds and one over the even integers. This turns your original sum into

\sum_{odd n} 1/n * 1/2^n + \sum_{even n} 1/n.

Hopefully you can take it from here. ^_^

Regards,
Kyle
.