Crossover-101(BITSAT-2015)

Calculus Level 5

Suppose \( \large \displaystyle A=\sum _{ n=0 }^{ \infty }{ \frac { 1 }{ (2n)! } } \).

Then which one of the following is equal to \(A^2\)?

  1. \(\large \displaystyle \frac{1}{2}+\sum _{ n=1 }^{ \infty }{ \frac { { 2 }^{ 2n-1 } }{ (2n)! } } \)

  2. \(\large \displaystyle \sum _{ n=0}^{ \infty }{ \frac { 1 }{ { ((2n)!) }^{ 2 } } } \)

  3. \(\large \displaystyle 1+\sum _{ n=1 }^{ \infty }{ \frac { { 2 }^{ 2n-1 } }{ (2n)! } } \)

  4. \(\large \displaystyle \frac{1}{2}+\sum _{ n=1 }^{ \infty }{ \frac { { 2 }^{ 2n} }{ (2n)! } } \)

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