1²+2²/1×2+2²+3²/2×3+……+2001²+2002²/2001×2002
问题描述：
1²+2²/1×2+2²+3²/2×3+……+2001²+2002²/2001×2002
答
考察一般项：[n²+(n+1)²]/[n(n+1)]=(2n²+2n+1)/(n²+n)=2 +1/(n²+n)=2+1/[n(n+1)]=2+1/n -1/(n+1) (1²+2²)/(1×2)+(2²+3²)/(2×3)+……+(2001²+2002²)/(2001...