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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