首先算
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+3^3+……+n^2)+(1+2+3+……+n)
=n(n+1)(2n+1)/6+n(n+1)/2
=n(n+1)(n+2)/3
它展开式的三次项系数为1/3
lim [1*2+2*3+3*4+...+n*(n+1)]/n^3＝1/3
lim [1*2+2*3+3*4+...+n*(n+1)]/n^3之值
1个回答
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