Question

有理数的巧算 快~~

1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+.....+1/(1+2+3+4+5+6....+100)

1为分子,括号里的为分母
因为不知道分数怎么打,就用“/”代替分数线了
谢谢大家拉~~~~~~
要快哦~~~~

Answer 1

1+1/(1+2)+1/(1+2+3)+1/(1+2+3+4)+.....+1/(1+2+3+4+5+6....+100)
=1+1/3+1/[（1+3）*3/2]+1/[(1+4)*4/2]+......+1/[(1+100)*100/2]
=1+1/3+2/(3*4)+2/(4*5)+2/(5*6)+.....+2/(100*101)
=1+1/3+2*(1/3-1/4)+2*(1/4-1/5)+.....+2*(1/100-1/101)
=1+1/3+2*(1/3-1/4+1/4-1/5+.....+1/99-1/100+1/100-1/101)
=1+1/3+2*(1/3-1/101)
=2-2/101
=200/101

Answer 2

哎!我想我能帮你,但是我用的手机,不方便写下来呀!希望有其它人能帮你,祝你好运!