Question

1/(1×2）+1/(2×3）+1/(3×4）......+1/（48×49）+1/(49×50）等于多少？

Answer 1

可以如下分析思考：

1/(1×2）+1/(2×3）+1/(3×4）......+1/（48×49）+1/(49×50）
= (1 -1/2) + (1/2 - 1/3) + (1/3 - 1/4) + ... + (1/48 - 1/49 + (1/49 - 1/50)
= 1 - 1/50
= 49/50

Answer 2

由
1/(1×2)=(1/1)-(1/2)；
1/(2×3)=(1/2)-(1/3)；
1/(3×4)=(1/3)-(1/4)；
从上可以看出，等式左边可以拆成二个分母组成的分式之差，分子都为1,分母分别为为n和n+1
1/[n(n+1)]=(1/n)-[1/(n+1)]

1-1/50=49/50