1×2分之1+2×3分之1+3×4分之1······+8×9分之1+9×10分之1

问题描述:

1×2分之1+2×3分之1+3×4分之1······+8×9分之1+9×10分之1

常规算法:
1/(1x2) + 1/(2x3)+1/(3x4)+...+1/(8x9) + 1/(9x10)
=(1/1 -1/2) + (1/2 -1/3) + (1/3 -1/4) +...+(1/8-1/9) +(1/9-1/10)
=1/1 - 1/10
=9/10