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Manipal MET2016MathematicsSequences and Series

1+ 2^3 2! + 3^3 3! + 4^3 4! + equals

Options

  1. A5 e
  2. B4 e
  3. C3 e
  4. D2 e

Correct answer

A. 5 e

Step-by-step solution

Here, T_n= n^3 n! = n^2-1 (n-1)! + 1 (n-1)! aligned & = n+1 (n-2)! + 1 (n-1)! & = 1 (n-3)! + 3 (n-2)! + 1 (n-1)! aligned T_n= ( 1 (n-3)! + 3 (n-2)! + 1 (n-1)! )=e+3 e+e=5 e

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