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JEE Math Practice Question

The sum $$\sum\limits_{n = 1}^\infty {{{2{n^2} + 3n + 4} \over {(2n)!}}} $$ is equal to :

  1. A.$${{11e} \over 2} + {7 \over {2e}}$$
  2. B.$${{13e} \over 4} + {5 \over {4e}} - 4$$
  3. C.$${{11e} \over 2} + {7 \over {2e}} - 4$$
  4. D.$${{13e} \over 4} + {5 \over {4e}}$$

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