1/2+1/6+1/12+1/20+······+1/72+1/90）（计算）

Answer 1

解答：
就是裂项，将分数写成两个分数的和
1/2+1/6+1/12+1/20+······+1/72+1/90
=1/(1*2)+1/(2*3)+1/(3*4)+1/(4*5)+1/(5*6)+1/(6*7)+1/(7*8)+1/(8*9)+1/(9*10)
=(1/1-1/2)+(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+(1/5-1/6)+(1/6-1/7)+(1/7-1/8)+(1/8-1/9)+(1/9-1/10)
=1-1/10
=9/10