Question

(1+2+3+4/1)+(1+2+3+4+5/1)+(1+2+3+4+5+6/1)+.+(1+2+3+4+.+99/1)

Answer 1

问题是不是：[1/(1+2+3+4)+1/(1+2+3+4+5)+……+1/(1+2+3+……+99)]=?

1+2+3+……+n=n*(n+1)/2

1/(1+2+3+……=n)=2/[n*(n+1)]=2*[1/n-1/(n+1)]

故,原式=2*[(1/4-1/5)+(1/5-1/6)+……+(1/99-1/100)]

=2*(1/4-1/100)

=12/25

完毕.