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Manipal MET2021MathematicsSequences and Series

1+ 3 1! + 5 2! + 7 3! + is

Options

  1. A5
  2. B2 e
  3. C3 e
  4. DNone of these

Correct answer

C. 3 e

Step-by-step solution

Let T_n be the n th term of a given series: T_n= (2 n-1) (n-1)! ; n=1,2,3, , aligned T_n & = 2 n (n-1)! - 1 (n-1)! & =2 [ (n-1) (n-1)! + 1 (n-1)! ]- 1 (n-1)! & = 2 (n-2)! + 1 (n-1)! _ n=1 ^ T_n & = _ n=1 ^ 2 (n-2)! + _ n=1 ^ 1 (n-1)! & =2 e+e=3 e aligned

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