已知1/6=1/2-1/3、1/12=1/3-1/4、......你能根据这个规律很快算出1/6+1/12+1/20+......+1/9900的结果吗？

1/6+1/12+1/20+...+1/9900
=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+...+(1/99-1/100)
=1/2-1/3+1/3-1/4+1/4-1/5+...+1/99-1/100
=1/2-(1/3-1/3)-(1/4-1/4)-(1/5-1/5)-...-(1/99-1/99)-1/100
=1/2-0-0...-0--0-1/100
=1/2-1/100
=49/100本回答被提问者和网友采纳

1/6+1/12+1/20+...+1/9900
=(1/2-1/3)+(1/3-1/4)+(1/4-1/5)+...+(1/99-1/100)
=1/2-1/100
=49/100