设{an}是等差数列,an=2n-1,{bn}是等比数列,bn=2^(n-1)求{an/bn}前n项和Sn

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设{an}是等差数列,an=2n-1,{bn}是等比数列,bn=2^(n-1)求{an/bn}前n项和Sn
设{an}是等差数列,an=2n-1,{bn}是等比数列,bn=2^(n-1)求{an/bn}前n项和Sn

设{an}是等差数列,an=2n-1,{bn}是等比数列,bn=2^(n-1)求{an/bn}前n项和Sn
s(n)=(2*1-1)/1 + (2*2-1)/2 + (2*3-1)/2^2 + ...+ [2(n-1)-1]/2^(n-2) + (2n-1)/2^(n-1)
2s(n)=2(2*1-1)/1 + (2*2-1)/1 + (2*3-1)/2 + ...+ [2(n-1)-1]/2^(n-3) + (2n-1)/2^(n-2),
s(n)=2s(n)-s(n)=2(2*1-1)/1 + (2*1)/1 + (2*1)/2 + ...+ [2*1]/2^(n-2) - (2n-1)/2^(n-1)
=2 + 2[1+1/2+...+1/2^(n-2)] - (2n-1)/2^(n-1)
=2+4[1-1/2^(n-1)] - (2n-1)/2^(n-1)
=6 - (2n+3)/2^(n-1)

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