举报
xiaoaima
哈 你太懒了 Dn = a1a2...a(n-1) + anD(n-1) = a1a2...a(n-1) + an[a1a2...a(n-2) + a(n-1)D(n-2)] = a1a2...a(n-1) + a1a2...a(n-2)an + ana(n-1)D(n-2) = ...... = a1a2...a(n-1) + a1a2...a(n-2)an + ... + a1a3...an + ana(n-1)....a2D1 = a1a2...a(n-1) + a1a2...a(n-2)an + ... + a1a3...an + ana(n-1)....a2(1+a1) = a1a2...a(n-1) + a1a2...a(n-2)an + ... + a1a3...an + a2a2...an +a1a2...an = a1a2...an/an + a1a2...an/a(n-1)+ ...+a1a2...an/a2 + a1a2...an/a1 + a1a2...an = a1a2...an(1+1/a1+1/a2+...+1/an). 归纳法就很自然了, 你自己应该会写的