{an}是等比数列,a2=2,a5=1/4,求a1a2+a2a3+...+anan+1

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{an}是等比数列,a2=2,a5=1/4,求a1a2+a2a3+...+anan+1
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{an}是等比数列,a2=2,a5=1/4,求a1a2+a2a3+...+anan+1
{an}是等比数列,a2=2,a5=1/4,求a1a2+a2a3+...+anan+1

{an}是等比数列,a2=2,a5=1/4,求a1a2+a2a3+...+anan+1
a2a3/a1a2=a3/a1=q^2
a5/a2=q^3=1/8,
q=1/2,q^2=1/4,
a1=a2/q=2/(1/2)=4,
a1a2=4*2=8,
a1a2+a2a3+...+anan+1
=8[1-(1/4)^2n]/(1-1/4)
=32[1-(1/4)^2n]/3