IIT JEE , AIEEE Forum - Mathematics , Algebra

hash_include

1.
$\sum_{i=1}^{n} \frac 1 {\frac {r(r+1)}{2}}$

$= 2. \sum_{i=1}^{n} \frac 1{r(r+1)}$

$= 2. \sum_{i=1}^{n} \frac {(r+1) - r }{r(r+1)}$

$= 2. [\sum_{i=1}^{n} \frac 1 {r} - \sum_{i=1}^{n} \frac 1 {r+1}]$

$= 2[ (\frac 1 1 - \frac 1 2) + (\frac 1 2 - \frac 1 3) ....... + (\frac 1 n - \frac 1 {n+1})]$

everything except the first and last term gets cancelled

$= 2 ( 1 - \frac 1 {n+1})$

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

Smile

Ask & Discuss Questions with Community & Experts