简便运算:3/1 15/1 63分之1 99分之1 143分之1
问题描述：
简便运算:3/1 15/1 63分之1 99分之1 143分之1
答
1/n(n+2)=1/2*(1/n-1/(n+2)
1/3+1/15+1/35+1/63+1/99+1/143
=1/2(1-1/3+1/3-1/5+1/5-1/7+1/7-1/9+1/9-1/11+1/11-1/13)
=1/2(1-1/13)
=1/2*12/13
=6/13
答
原式应为"1/3+1/15+1/35+.+1/143
=1/2[1-1/3+1/3-1/5+1/5-1/7+...+1/11-1/13]
=1/2(1-1/13)
=6/13
*****应用了1/n(n+2)=1/2[1/n-1/(n+2)]