1/1×3+1/3×5+1/5×7+···+1/(2n-1)(2n+1)
问题描述:
1/1×3+1/3×5+1/5×7+···+1/(2n-1)(2n+1)
答
1/﹙1×3﹚+1/﹙3×5﹚+1/﹙5×7﹚+……+1/﹙2n-1﹚﹙2n+1﹚
=1/2×[1-1/3+1/3-1/5+1/5-1/7+……+1/﹙2n-1﹚-1/﹙2n+1﹚]
=1/2×[1-1/﹙2n+1﹚]
=1/2×2n/﹙2n+1﹚
=n/﹙2n+1﹚.