Tính tổng: 1/6+1/24+1/60+1/120+...+1/1320

* Hướng dẫn giải

Gọi tổng đã cho là A.

Ta có:
A =$\frac{1}{1}$x2x3 + $\frac{1}{2}$x3x4 + $\frac{1}{3}$x4x5 +$\frac{1}{4}$x5x6 .... + $\frac{1}{10}$x11x12
Chú ý rằng: 
$\frac{1}{1}$x2x3 = $\frac{1}{2}$ x($\frac{1}{1}$x2 $-\frac{1}{2}$x3)
$\frac{1}{2}$x3x4 =$\frac{1}{2}$x ($\frac{1}{2}$x3 $-\frac{1}{3}$x4)
$\frac{1}{3}$x4x5 = $\frac{1}{2}$ x ($\frac{1}{3}$x4 $-\frac{1}{4}$x5)
..........
Từ đó suy ra: 
A = $\frac{1}{2}$ x ($\frac{1}{1}$x2 $-\frac{1}{2}$x3 + $\frac{1}{2}$x3 $-\frac{1}{3}$x4+$\frac{1}{3}$x4 $-\frac{1}{4}$x5+...+ $\frac{1}{10}$x11 $-\frac{1}{11}$x12)

= $\frac{1}{2}$ x ($\frac{1}{1}$x2 $-\frac{1}{11}$x12)

=$\frac{1}{2}$ x ($\frac{1}{2}$ $-\frac{1}{132}$)

= $\frac{65}{264}$