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AP EAMCET2001MathematicsSequences and Series

2 2 ! + 2+4 3 ! + 2+4+6 4 ! + is equal to

Options

  1. Ae
  2. Be⁻¹
  3. Ce⁻²
  4. De⁻³

Correct answer

A. e

Step-by-step solution

We have, aligned T_n & = 2+4+6+ +2 n (n+1) ! T_n & = 2 n (n+1) ! = 2 n(n+1) 3 (n+1) n(n-1) ! & = 1 (n-1) ! aligned aligned S & =T₁+T₂+T₃+ & =1+1+ 1 2 ! + 1 3 ! + =e aligned

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