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TIFR-2013-Maths-B: 20

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True/False Question :

Consider the function $f\left ( x \right )=ax+b$ with $a,b\in \mathbb{R}$. Then the iteration 

$$x_{n+1}=f\left ( x_{n} \right ); \: \:\:\:\:\:n\geq 0$$

for a given $x_{0}$ converges to $b/\left ( 1-a \right )$ whenever $0<a<1.$

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