Thread: [SOLVED] Sum of infinite series

1. [SOLVED] Sum of infinite series

Determine whether the given infinite series converges or diverges. If it converges, find its sum.

$
\sum_{n=1}^{\infty}\frac{2n}{\sqrt{4n^2+3}}
$

Any help is greatly appreciated!

2. Hi

You should try to take $4n^2$ out of the square root to find the limit of $\frac{2n}{\sqrt{4n^2+3}}$ when $n\to \infty$.

3. Originally Posted by flyingsquirrel
Hi

You should try to take $4n^2$ out of the square root to find the limit of $\frac{2n}{\sqrt{4n^2+3}}$ when $n\to \infty$.
How do I take $4n^2$ out of the square root?

4. You can factor $4n^2$ : $\sqrt{4n^2+3}=\sqrt{4n^2\left(1+\frac{3}{4n^2}\rig ht)}
=\sqrt{4n^2}\sqrt{1+\frac{3}{4n^2}}=\ldots$

5. Originally Posted by flyingsquirrel
You can factor $4n^2$ : $\sqrt{4n^2+3}=\sqrt{4n^2\left(1+\frac{3}{4n^2}\rig ht)}
=\sqrt{4n^2}\sqrt{1+\frac{3}{4n^2}}=\ldots$

I see what I need to do now. Thank you!