A= 1/2 + 1/6 +1/12+1/20+1/30+...+1/n A=49/50 Tìm n.

* Hướng dẫn giải

$\frac{1}{2}$= $\frac{1}{\left(1x2\right)}$ = 1 - $\frac{1}{2}$
$\frac{1}{6}$ = $\frac{1}{\left(2x3\right)}$= $\frac{1}{2}$ - $\frac{1}{3}$
$\frac{1}{12}$= $\frac{1}{\left(3x4\right)}$ = $\frac{1}{3}$ - $\frac{1}{4}$
........
$\frac{1}{n}$= $\frac{1}{\left(nx\right(n+1\left)\right)}$= 1/n - $\frac{1}{(n+1)}$
$\frac{1}{2}$+ $\frac{1}{6}$+ $\frac{1}{12}$+ $\frac{1}{20}$ + $\frac{1}{30}$ +...+ $\frac{1}{n}$= 1 - $\frac{1}{2}$+ $\frac{1}{2}$ - $\frac{1}{3}$+ $\frac{1}{3}$- $\frac{1}{4}$+...+$\frac{1}{n}$- $\frac{1}{(n+1)}$ = $\frac{49}{50}$
Hay A = 1 - $\frac{1}{(n+1)}$= $\frac{49}{50}$
=> $\frac{1}{(n+1)}$ = 1 - $\frac{49}{50}$
$\frac{1}{(n+1)}$= $\frac{1}{50}$
Suy ra n+1=50 nên n=49