求(1/1×3×5)+(1/3×5×7)+……+1/(2n~1).(2n+1).(2n+3)的极限?
问题描述：
求(1/1×3×5)+(1/3×5×7)+……+1/(2n~1).(2n+1).(2n+3)的极限?
答
(1/1×3×5)+(1/3×5×7)+……+1/(2n~1).(2n+1).(2n+3)
=1/4 [1/1×3-1/3×5+1/3×5-1/5×7+.+1/(2n-1)(2n+1)-1/(2n+1)(2n+3)]
=1/4[1/3-1/(2n+1)(2n+3)]
所以
原式的极限=lim(n->∞)1/4[1/3-1/(2n+1)(2n+3)]=1/4×1/3=1/12