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If `a_(0)=x,a_(n+1)=f(a_(n)), " where " n=0,1,2, …,` then answer the following questions. If `f(x)=(1)/(1-x),` then which of the following is not true?A. `a_(n)=(1)/(1-x) " if " n=3k+1`B. `a_(n)=(x-1)/(x) " if " n=3k+2`C. `a_(n)=x " if " n=3k`D. None of these |
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Answer» Correct Answer - D Given `a_(n+1)=f(a_(n))` Now, `a_(1)=f(a_(0))=f(x)` `or a_(2)=f(a_(1))=f(f(a_(0)))=fof(x)` `or a_(n)=(fofofof …f(x))/("n times")` Now, if `f(x)=(1)/(1-x), fof(x)=(1)/(1-(1)/(1-x))=(x-1)/(x)` or `fofof(x)=((1)/(1-x)-1)/((1)/(1-x))=x` `or a_(n)=(fofof ... of(x))/("n times")=(1)/(1-x) " if " n=3k+1` `=(x-1)/(x) " if " n=3k+2` `=x " if " n=3k` |
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