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TIFR-2013-Maths-B: 12

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TIFR-2013-Maths-B: 11
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True/False Question : Let $x_{1}\in\left ( 0,1 \right )$ be a real number between $0$ and $1$. For $n> 1$, define $x_{n+1}=x_{n}-x_{n}^{n+1}.$ Then $\underset{n\rightarrow \infty }{lim}x_{n}$ exists.
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