Tính nhanh :3/1x2 + 3/2x3 + 3/3x4 + 3/4x5 + 3/5x6 +...+ 3/9x10 + 77/2x9 + 77/9x16 + 77/16x23 +...+77/93x100

Lời giải:

`3/(1xx2)+3/(2xx3)+3/(3xx4)+3/(4xx5)+3/(5xx6)+...+3/(9xx10)+77/(2xx9)+77/(9xx16)+77/(16xx23)+...+77/(93xx100)`

`=(3/(1xx2)+3/(2xx3)+3/(3xx4)+3/(4xx5)+3/(5xx6)+...+3/(9xx10))+(77/(2xx9)+77/(9xx16)+77/(16xx23)+...+77/(93xx100))`

`=3xx(1/(1xx2)+1/(2xx3)+1/(3xx4)+1/(4xx5)+1/(5xx6)+...+1/(9xx10))+11xx(7/(2xx9)+7/(9xx16)+7/(16xx23)+...+7/(93xx100))`

`=3xx(1-1/2+1/2-1/3+1/3-1/4+1/4-1/5+1/5-1/6+...+1/9-1/10)+11xx(1/2-1/9+1/9-1/16+1/16-1/23+...+1/93-1/100)`

`=3xx(1-1/10)+11xx(1/2-1/100)`

`=3xx(10/10-1/10)+11xx(50/100-1/100)`

`=3xx9/10+11xx49/100`

`=27/10+539/100`

`=270/100+539/100`

`=809/100`