(1/1+2)+(1/1+2+3)+```+1/(1+2+3+...+100)=?怎么解答
(1/1+2)+(1/1+2+3)+```+1/(1+2+3+...+100)=?怎么解答
日期：2021-06-01 20:54:00 人气：1
An=1/(1+2+...+(n+1))
=2/(n+1)(n+2)
=2[1/(n+1)-1/(n+2)]
(1/1+2)+(1/1+2+3)+```+1/(1+2+3+...+100)
=2[1/2-1/3+1/3-1/4+...+1/(100)-1/(101)]
=2[1/2-1/(101)]
=99/101
=2/(n+1)(n+2)
=2[1/(n+1)-1/(n+2)]
(1/1+2)+(1/1+2+3)+```+1/(1+2+3+...+100)
=2[1/2-1/3+1/3-1/4+...+1/(100)-1/(101)]
=2[1/2-1/(101)]
=99/101