 | > f(x)=Σ[n=1→∞]na^(n-1)*(1-x)^n
g(x)=Σ[n=1→m]na^(n-1)*(1-x)^n
=(1-x)Σ[n=1→m]n{a-ax}^(n-1)
(a-1)/a<x<(a+1)/aより -1<ax-a<1 ∴|a-ax|<1
g(x)-(a-ax)g(x)=(1-x)Σ[n=1→N]{n{a-ax}^(n-1)-(n-1)n{a-ax}^(n-1)}
=(1-x)Σ[n=1→N]{a-ax}^(n-1)=(1-x){1-(a-ax)^N}/{1-(a-ax)}
g(x)=(1-x){1-(a-ax)^N}/{1-(a-ax)}^2
∴f(x)=lim[N→∞]g(x)=(1-x)/{ax-a+1}^2
[2] f(x)-1/[a(ax-a+1)]-m=0
⇔(1-x)/{ax-a+1}^2-1/[a(ax-a+1)]-m=0
⇔-a(1-x)-(ax-a+1)-ma{ax-a+1}^2=0
⇔-1-ma{ax-a+1}^2=0
⇔ma^3x^2-2ma^2(a-1)x+ma(a-1)^2+1=0
D={-2ma^2(a-1)}^2-4(ma^3)(ma(a-1)^2+1)>0
⇔{4m^2a^4(a-1)^2}-4(ma^3)(ma(a-1)^2+1)>0
-4(ma^3)>0
∴m<0
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