1/2+1/6+1/12+1/20......+1/90 怎么算，讲清楚点谢谢！

Answer 1

解：
观察可知：
1/2 = 1/(1×2) = 1 - (1/2)
1/6 = 1/(2×3) = (1/2) - (1/3)
1/12 = 1/(3×4) = (1/3) - (1/4)
1/20 = 1/(4×5) = (1/4) - (1/5)
.......
1/90 = 1/(9×10) = (1/9) - (1/10)
因此：
原式 = 1 - (1/2)+(1/2) - (1/3)+(1/3) - (1/4)+(1/4) - (1/5)+.....+(1/9) - (1/10)
上式中间项都消掉了，因此：
原式 = 1 - (1/10) = 9/10

Answer 2

1/2=1/（1×2）=1-1/21/6=1/（2×3）=1/2-1/31/12=1/（3×4）=1/3-1/4……1/90=1/（9×10）=1/9-1/10所以1/2+1/6+1/12+1/20......+1/90=(1-1/2)+(1/2-1/3)+(1/3-1/4)+……+（1/9-1/10）=1-1/10=9/10