第13题怎么解啊?

1个回答

  • 假设q=1,则A2=A3,A2×A3=A2^2>0,不符合题意

    q≠1

    A1+A2+A3+A4=A1×(1-q^4)/(1-q)

    {1/An}是首项为1/A1,公比为1/q的等比数列

    1/A1+1/A2+1/A3+1/A4=(1/A1)×(1-1/q^4)/(1-1/q)

    两式相除

    A1×(1-q^4)/(1-q)/[(1/A1)×(1-1/q^4)/(1-1/q)]

    =A1^2×q^4/q×(1-q^4)/(1-q)/[(q^4-1)/(q-1)]

    =A1^2×q^3

    =A2×A3=-9/8

    1/A1+1/A2+1/A3+1/A4

    =(A1+A2+A3+A4)/(A2×A3)

    =(15/8)/(-9/8)

    =-5/3