设插入的n个数为a1,a2,.,an则1/n,a1,a2,........,an, n+1成等比数列根据等比数列的性质： a1*an=a2*a(n-1)=........=1/n*(n+1)设Tn=a1*a2*........an则Tn=an*a(n-1)*.......*a1∴T2n=(a1*an)*(a2*a(n-1))*.......(an*a1)
=(n+1)/n *(n+1)/n*......*(n+1)/n
=[(n+1)/n]^n∴Tn=√[(n+1)/n]^n=(1+1/n)^(n/2)...
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