T = `\frac{1}{1x2}` +$\frac{1}{2x3}$ +$\frac{1}{3x4}$ + .... + $\frac{1}{99x100}$
ta có :
$\frac{1}{1 x 2}$ = `1/1` - `1/2`
$\frac{1}{2 x 3}$ = `1/2` - `1/3`
$\frac{1}{3 x 4}$ = `1/3` - `1/4`
...........
$\frac{1}{99 x 100}$ = `1/99` - `1/100`
⇒ T = `\frac{1}{1x2}` +$\frac{1}{2x3}$ +$\frac{1}{3x4}$ + .... + $\frac{1}{99x100}$
= `1/1` - `1/2` + `1/2` - `1/3` + `1/3` - `1/4` +..... + `1/99` - `1/100`
= `1/1` - `1/100`
= `100/100` - `1/100`
= `99/100`
Vậy T = `99/100`
