计算(2/1×2×3)+(2/2×3×4)+(2/3×4×5)+(2/4×5×6)+……+(2/99×100×101)+(2/100×101×102)
问题描述:
计算(2/1×2×3)+(2/2×3×4)+(2/3×4×5)+(2/4×5×6)+……+(2/99×100×101)+(2/100×101×102)
答
原式=1/1×2-1/2×3+1/2×3-1/3×4+……+1/100×101-1/101×102
=1/1×2-1/101×102
=2575/5151