1*2的平方+2*3的平方+3*4的平方+.+19*20的平方是多少?
人气：188 ℃ 时间：2020-04-18 13:08:13
解答
an = n(n+1)^2= n(n+1)(n+2) -n(n+1)=(1/4)[n(n+1)(n+2)(n+3)-(n-1)n(n+1)(n+2)] - (1/3)[n(n+1)(n+2) -(n-1)n(n+1)]Sn = a1+a2+...+an =(1/4)n(n+1)(n+2)(n+3) - (1/3)n(n+1)(n+2)1.2^2+2.3^2+...+...
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