n(n+1)=n^2+n
所以可以把原式化成两个数列的和
原式=(1+2+3+4+.+n)+(1^2+2^2+3^2+...+n^2)+n(n+2)
=n(n+1)/2+n(n+1)(2n+1)/6+n(n+2)
=[3n(n+1)+n(n+1)(2n+1)]/6+n(n+2)
1X2+2X3+...+n(n+1)+n(n+2)
2个回答
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