Question

1/2+5/6+11/12+19/20+...+9898/9900

Answer 1

这个倒不是很难

1/2+5/6+11/12+19/20+...+9898/9900

=（1-1/2)+(1-1/6)+(1-1/12)+……+(1-1/9900)

= 99 - (1/(1*2)+1/(2*3)+……+1/(99*100))

= 99 - (1-1/2+1/2-1/3+……+1/99-1/100)

= 99 - (1-1/100)

= 99 - 99/100

= 98又1/100

这道题目是通过裂项来解决的.