题目

(3²+1²)/(3²-1²)+(5²+1)/(5²-1)+(7²+1)/7²-1)+……+（1995²+1)/(1995²-1)=

提问时间：2021-04-01

答案

(3²+1²)/(3²-1²)=1+2/[2×4]=1+（4-2）/[2×4]1+1/2-1/4
(5²+1)/(5²-1)=1+2/(5²-1)=1+(6-4)/[4×6]=1+1/4-1/6
.
（1995²+1)/(1995²-1)=1+（1996-1994）/[1994×1996]=1+1/1994-1/1996
(3²+1²)/(3²-1²)+(5²+1)/(5²-1)+(7²+1)/7²-1)+……+（1995²+1)/(1995²-1)
=997+1/2-1/1996
=997又997/1996