等差数列{An}的各项均为正数,A1=3,数列的前n项和为Sn,等比数列{Bn}中,b1=1.,且b2*S2=64,{Ban}是公比为64的等比数列.(1)求An与Bn.(2)证明1/S1+1/S2+……+1/Sn

等差数列{An}的各项均为正数,A1=3,数列的前n项和为Sn,等比数列{Bn}中,b1=1.,且b2*S2=64,{Ban}是公比为64的等比数列.(1)求An与Bn.(2)证明1/S1+1/S2+……+1/Sn
等差数列{An}的各项均为正数,A1=3,数列的前n项和为Sn,等比数列{Bn}中,b1=1.,且b2*S2=64,{Ban}是公比为64的等比数列.(1)求An与Bn.(2)证明1/S1+1/S2+……+1/Sn

等差数列{An}的各项均为正数,A1=3,数列的前n项和为Sn,等比数列{Bn}中,b1=1.,且b2*S2=64,{Ban}是公比为64的等比数列.(1)求An与Bn.(2)证明1/S1+1/S2+……+1/Sn
q=4,d=3
an=3n
bn=4^(n-1)
(2)Sn=3/2*n(n+1)
故左边=2/3*{1/（1*2）+1/（2*3）+...+1/[n(n+1)]}
=2/3*{[1-1/2]+[1/2-1/3]+[1/3-1/4]+...+[1/2-1/(n+1)]}
=2/3*[1-1/(n+1)]