Question

1/1*2+1/2*3+1/3*4+…+1/1993*1994 1/3+1/15+1/35+1/63+...+1/17*19

谁告诉我追加悬赏
1/3+1/15+1/35+1/63+...+1/17*19

Answer 1

1/(1*2)=1-1/2
1/(2*3)=1/2-1/3
......
1/1*2+1/2*3+1/3*4+…+1/1993*1994 1/3+1/15+1/35+1/63+...+1/逗穗宴17*19
=1-1/2+1/2-1/族喊3+...+1/17-1/19
=1-1/山银19
=18/19

追问

谢谢 还有一道题

追答

1/3+1/15+1/35+1/63+...+1/17*19
=1/(1*3)+1/(3*5)+...+1/(17*19)
=1/2*(1-1/3+1/3-1/5+...+1/17-1/19)
=1/2*(1-1/19)
=1/2*18/19
=9/19