在等比数列{an}中,若a1+a2+a3+a4+a5=31/16,a3=1/4,1/a1+1/a2+1/a3+1/a4+1/a5=
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解:
a1+a2+a3+a4+a5=31/16,a3=1/4
1/4/q^2 + 1/4/q +1/4 +1/4*q +1/4*q^2=31/16
1/4*(1/q^2+1/q+1+q+q^2)=31/16
1/q^2+1/q+1+q+q^2=31/4
1/a1+1/a2+1/a3+1/a4+1/a5
=1/(1/4/q^2)+1/1/4/q+1/(1/4)+1/(1/4*q)+1/(1/4*q^2)
=4q^2+4q+4+4/q+4/q^2
=4(q^2+q+1+1/q+1/q^2)
=4*31/4
=31
a1+a2+a3+a4+a5=31/16,a3=1/4
1/4/q^2 + 1/4/q +1/4 +1/4*q +1/4*q^2=31/16
1/4*(1/q^2+1/q+1+q+q^2)=31/16
1/q^2+1/q+1+q+q^2=31/4
1/a1+1/a2+1/a3+1/a4+1/a5
=1/(1/4/q^2)+1/1/4/q+1/(1/4)+1/(1/4*q)+1/(1/4*q^2)
=4q^2+4q+4+4/q+4/q^2
=4(q^2+q+1+1/q+1/q^2)
=4*31/4
=31
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