$\displaystyle { For \ n \in N \ let \ \ x_n = \frac {1}{1+n} + \frac {1}{2+n} +...+\frac {1}{2n} : }$

$\displaystyle a- \ show \ \ that \ \ x_n \ \ is \ \ increasing .$

$\displaystyle b- \ prove \ \ that \ \ x_n < 1 , \ \forall n \in N .$

$\displaystyle c- \ conclude \ \ that \ \ x_n \ \ is \ \ convergent$