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﹚.
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﹚.