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TIFR-2016-Maths-A: 1

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The value of the product $\left ( 1+\frac{1}{1!} +\frac{1}{2!}+\cdots \right )\left ( 1-\frac{1}{1!} +\frac{1}{2!}-\frac{1}{3!}+\cdots \right )$ is 

  1. $1$
  2. $e^{2}$
  3. $0$
  4. $log_{e} \:2$.
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