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The sum of the infinite series 2² 2 ! + 2⁴ 4 ! + 2⁶ 6 ! + is equal to

Options

  1. Ae ²+1 2 e
  2. Be ⁴+1 2 e ²
  3. C( e ²-1 )² 2 e ²
  4. D( e ²+1 )² 2 e ²

Correct answer

C. ( e ²-1 )² 2 e ²

Step-by-step solution

We know that e^ x +e^ -x 2 =1+ x² 2 ! + x⁴ 4 ! + x⁶ 6 ! + keeping x =2 , we get Expression = 1 2 [ e²+e⁻² 2 ]-1= (e²-1 )² 2 e²

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