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Manipal MET2012MathematicsSequences and Series

The sum of the series 1+ 2^2 2! + 3^2 3! + 4^2 4! + is

Options

  1. A2 e
  2. B3 e
  3. C2 e-1
  4. DNone of these

Correct answer

A. 2 e

Step-by-step solution

aligned & Let S=1+ 2^2 2! + 3^2 3! + 4^2 4! + & T_n= n^2 n! = n (n-1)! & T_n= n-1+1 (n-1)! = 1 (n-2)! + 1 (n-1)! & S_n= T_n= 1 (n-2)! + 1 (n-1)! & =e+e & =2 e aligned

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