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AP EAMCET2005MathematicsSequences and Series

_ n=1 ^ 2 n^2+n+1 n ! is equal to

Options

  1. A2 e-1
  2. B2 e+1
  3. C6 e-1
  4. D6 e+1

Correct answer

C. 6 e-1

Step-by-step solution

aligned & Let S= _ n=1 ⁻ 2 n^2+n+1 n ! & = _ n=1 ( 2 n (n-1) ! + 1 (n-1) ! + 1 n ! ) & = _ n=1 ( 2 (n-2) ! + 3 (n-1) ! + 1 n ! ) & =2 (1+ 1 1 ! + 1 2 ! + 1 3 ! + ) & +3 (1+ 1 1 ! + 1 2 ! + )+ ( 1 1 ! + 1 2 ! + 1 3 ! + ) & =2 e+3 e+e-1 & =6 e-1 & aligned

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