等差数列《An》中,An╱A2n是一个与n无关的常数,则该常数可能为?

∵﹛An﹜是等差数列
∴An=A1+(n-1)d
∴A2n=A1+(2n-1)d
∴An╱A2n=[A1+(n-1)d]/[A1+(2n-1)d]
=[A1+(2n-1)d-nd]/[A1-d+2nd]
=1-nd/[A1-d+2nd]
①d=0,An/A2n=1
②A1-d=0,∴An/A2n=1-nd/2nd=1-1/2=1/2
∴该常数可能为1或1/2
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