# Thread: Taking the Limit of Partial Sums

1. ## Taking the Limit of Partial Sums

Hi,

It's been a while since I've practiced limits :s

So I'm asked to find the limit of the sequence tan[4n*pi/(4+16n)]

I take the limit of the things inside the brackets then I will look at what happens at tan(lim.)

I break the fraction apart

lim(n->inf) 4n*pi/4 + lim(n->inf) 4n*pi/16n = inf + pi/4

Now, my question is, because one piece of the partial sum limit was infinity, does the whole thing inside the brackets go to infinity or pi/4? I thought it went to infinity, but I think my homework wants me to say it goes to pi/4 based on an example it gave.

Any help? Thanks

2. ## Re: Taking the Limit of Partial Sums

Originally Posted by Coop
So I'm asked to find the limit of the sequence tan[4n*pi/(4+16n)]

You need to review of basic algebra.

$\displaystyle \frac{{4n\pi }}{{4 + 16n}} = \frac{\pi }{{\frac{1}{n} + 4}}$

3. ## Re: Taking the Limit of Partial Sums

Originally Posted by Plato
You need to review of basic algebra.

$\displaystyle \frac{{4n\pi }}{{4 + 16n}} = \frac{\pi }{{\frac{1}{n} + 4}}$
Oh right, I don't even know why I thought I could break the fraction up like that, silly mistake.