1/2+1/6+1/12+1/20+.+1/90的答案是多少?最好有过程.最好有解说.

1/2+1/6+1/12+1/20+.+1/90的答案是多少?最好有过程.最好有解说.
1/2+1/6+1/12+1/20+.+1/90的答案是多少?最好有过程.
最好有解说.

1/2+1/6+1/12+1/20+.+1/90的答案是多少?最好有过程.最好有解说.
1/2+1/6+1/12+1/20+1/30+.+1/72+1/90
= 1/1*2 +1/2*3 +1/3*4 +...+1/8*9 +1/9*10
= (1/1 -1/2)+(1/2 -1/3)+...+(1/8 -1/9)+(1/9 -1/10)
= 1/1 -1/10
= 9/10