已知1/1×2+1/2×3+1/3×4+…+1/9×10=1-1/9=9/10运用类比法求得...1/1×2+1/2×3+1/3×4+…+类比求得1/1×2×3+1/2×3×4+...+1/100×101×102=?答案是2575（即25×103）/10302(即101×102),求解题思路··

Question

已知1/1×2+1/2×3+1/3×4+…+1/9×10=1-1/9=9/10 运用类比法求得...
1/1×2+1/2×3+1/3×4+…+类比求得 1/1×2×3+1/2×3×4+...+1/100×101×102=?
答案是2575（即25×103）/10302(即101×102),求解题思路··

Answer 1

1/(1×2×3) = (1 - 2/2 + 1/3) / 21/(2×3×4) = (1/2 - 2/3 + 1/4) / 21/(3×4×5) = (1/3 - 2/4 + 1/5) / 2.1/(100×101×102) = (1/100 - 2/101 + 1/102) / 2等号两端分别相加,得1/(1×2×3)+1/(2×3×4)+1/(3×...