数列证明题1

题目

数列证明题1
已知等比数列{an}的前n项的和为Sn,a1a2a3……an=Pn,1/a1+1/a2+1/a3+……+1/an=Tn,求证,（Pn)^2=(Sn/Tn)^n

答案

Sn=a1*(1-q^n)/(1-q)Pn=a1*(a1*q)*(a1*q^2).*(a1*q^(n-1))=a1^n*q^(n*(n-1)/2)Tn=1/a1+1/(a1*q)+.+1/(a1*q^(n-1))=1/a1*(1-1/q^n)/(1-1/q)故(Pn)^2=a1^2n*q^(n*(n-1))Sn/Tn=(a1*(1-q^n)/(1-q))/(1/a1*(1-1/q^n)/(1-1...