解
n(n+2)=n²+2n
∴sn
=(1²+2²+3²+……+n²)+2(1+2+3+……+n)
=n*(n+1)*(2n+1)/6+2×(1+n)n/2
=1/6n(n+1)(2n+1)+(1+n)n
=n(n+1)(1/3n+1/6+1)
=n(n+1)(1/3n+7/6)
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