Tính nhanh: 1 4/3 + 2 4/15 + 3 4/35 + 4 4/63 + 5 4/99

`1 4/3+2 4/15+3 4/35+4 4/63+5 4/99`

`=(1+2+3+4+5)+(4/3+4/15+4/35+4/63+4/99)`

`=15+(4/(1xx3)+4/(3xx5)+4/(5xx7)+4/(7xx9)+4/(9xx11))`

`=15+[(4/(1xx3)xx1/2+4/(3xx5)xx1/2+4/(5xx7)xx1/2+4/(7xx9)xx1/2+4/(9xx11)xx1/2)xx2]`

`=15+[(2/(1xx3)+2/(3xx5)+2/(5xx7)+2/(7xx9)+2/(9xx11))xx2]`

`=15+[(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11)xx2]`

`=15+[(1-1/11)xx2]`

`=15+(10/11xx2)`

`=15+20/11`

`=185/11`

Vậy `1 4/3+2 4/15+3 4/35+4 4/63+5 4/99=185/11`