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The sum 1+ 1+3 2! + 1+3+5 3! + 1+3+5+7 4! + upto terms, is equal to

Options

  1. A6 e
  2. B4 e
  3. C3 e
  4. D2 e

Correct answer

D. 2 e

Step-by-step solution

aligned & S =1+ 1+3 2! + 1+3+5 3! + & = _ r =1 ^ r ^2 r ! & = _ r =1 ^ ( r -1+1) ( r -1)! = _ r =2 ^ 1 ( r -2)! + _ r =1 ^ 1 ( r -1)! & =2 e aligned

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