# Math Help - series limit

1. ## series limit

$a_{n} = \frac{1}{n+1} + \frac{1}{n+2} + ... \frac{1}{2n}$

what is the limit ?

2. ## Hii

Im trying to learn the same things so make sure to check my answer with someone else here but what I noticed is that the difference between each term is 1. Doesn´t that imply that this is an aritmetic series?
There is a formula for that and that is $\sum{a_1}+{a_2}....+a_n = \frac{n(a_1+a_n)}{2}$

3. We have $a_{n+1}-a_n = \frac 1{2n+1}+\frac 1{2n+2}-\frac 1{n+1}
= \frac 1 {\left(2n+1\right)\left(2n+2\right)}$
so you can write
$a_n$ as a sum.
Then you will have to study the convergence of a serie.