在等比数列an中,a3=1,a5=1/4则a1a2+a2a3+a3a4+.+ana(n+1)=

A5/A3=q^2=1/4
q=±1/2
A1=A3/q^2=4
AnA(n+1)=A1×q^(n-1)×A1×q^n=(A1)^2×(q^2n)/q
q=1/2
AnA(n+1)=4^2×(1/4)^n/(1/2)=32/4^n=2^(5-2n)
A1A2+A2A3+……+AnA(n+1)=8×(1-1/4^n)/(1-1/4)=32/3-2^(5-2n)/3
q=-1/2
AnA(n+1)=4^2×(1/4)^n/(-1/2)=32/4^n=-2^(5-2n)
A1A2+A2A3+……+AnA(n+1)=-8×(1-1/4^n)/(1-1/4)=-32/3+2^(5-2n)/3