1/3+1/15+1/35+1/63+...+1/399=这样子的简便算法!
问题描述：
1/3+1/15+1/35+1/63+...+1/399=
这样子的简便算法!
答
1/3+1/15+1/35+1/63+...+1/399
=1/(2^2-1)+1/(4^2-1)+1/(6^2-1)+1/(8^2-1)+1/(10^2-1)+...+1/(20^2-1)
=[1/(2-1)-1/(2+1)]/2+[1/(4-1)-1/(4+1)]/2+[1/(6-1)-1/(6+1)]/2+[(8-1)-1/(8+1)]/2+...+[1/(20-1)-1/(20+1)]/2
=[1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+...+1/19-1/21]/2
=[1-1/21]/2
=10/21
楼上的答案是对的,但是计算过程有误