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ISI2015-MMA-58

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Let $\{a_n\}, n \geq 1$, be a sequence of real numbers satisfying $\mid a_n \mid \leq 1$ for all $n$. Define $A_n = \frac{1}{n}(a_1+a_2+\cdots+a_n)$, for $n \geq 1$. Then $\underset{n \to \infty}{\lim} \sqrt{n}(A_{n+1}-A_n)$ is equal to

  1. $0$
  2. $-1$
  3. $1$
  4. none of these
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