已知f(x)=x/(x 1),f1(x)=f(x),fn(x)=fn-1[fn-1(x)]求f100(x)的值

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已知f(x)=x/(x 1),f1(x)=f(x),fn(x)=fn-1[fn-1(x)]求f100(x)的值

已知f(x)=x/(x 1),f1(x)=f(x),fn(x)=fn-1[fn-1(x)]求f100(x)的值
已知f(x)=x/(x 1),f1(x)=f(x),fn(x)=fn-1[fn-1(x)]
求f100(x)的值

已知f(x)=x/(x 1),f1(x)=f(x),fn(x)=fn-1[fn-1(x)]求f100(x)的值
f1(x)=f(x)=x/1-x=x/(1-x) f2(x)=f1(f1(x))=f1(f(x)=f1(x/1-x)=(x/1-x)/[1-(x/1-x)] =x/(1-2x) f3(x)=f2(f2(x))=f2(x/1-2x)=(x/1-2x)/[1-2(x/1-2x)] =x/(1-4x) f4(x)=f3(f3(x))=f3(x/1-4x)=(x/1-4x)/[1-4(x/1-4x)] =x/(1-8x) fn(x)=x/(1-2^(n-1)) 把100带进去就好了

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