1乘2加2乘3加3乘4，一直加到n乘(n+1)
=2乘2加3乘3加4乘4，一直加到(n+1)乘(n+1)-[2+3+4+ (n+1)]
=(n+1)(n+2)(2n+3)/6-1)-[2+3+4+ (n+1)]
=(n+1)(n+2)(2n+3)/6-(n+1)(n+2)/2
=(n+1)(n+2)2n
=2n(n+1)(n+2)
an=n(n+1)=n²+n
所以Sn=(1²+2²+……+n²)+(1+2+……+n)
=n(n+1)(2n+1)/6+n(n+1)/2
=n(n+1)(n+2)/3
1×2+2×3+3×4+……+n(n+1)
=1^2+1+2^2+2+3^2+3+……+n^2+n
=1^2+2^2+……+n^2+1+2+3+……+n
=n(n+1)(2n+1)/6+n(n+1)/2
=n(n+1)(n+2)/3
1*2+2*3+3*4+……+n(n+1)
=1^2+2^2+……+n^2+1+2+3+……+n
=n(n+1)(2n+1)/6+n(n+1)/2
=n(n+1)(n+2)/3
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