1. ## analysis

${ For \ n \in N \ let \ \ x_n = \frac {1}{1+n} + \frac {1}{2+n} +...+\frac {1}{2n} : }$
$a- \ show \ \ that \ \ x_n \ \ is \ \ increasing .$
$b- \ prove \ \ that \ \ x_n < 1 , \ \forall n \in N .$
$c- \ conclude \ \ that \ \ x_n \ \ is \ \ convergent$

2. Originally Posted by flower3
huh? what's this? are you implying we should do your homework?

show some progress then, but, for a start, put $a_n=\sum_{j=1}^n\frac1{n+j}$ and for $1\le j\le n$ we have $\frac1{2n}\le\frac1{n+j}\le\frac1{n+1}.$