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AP EAMCET2003MathematicsSequences and Series

1 2 ! + 1+2 3 ! + 1+2+3 4 ! + is equal to :

Options

  1. Ae 2
  2. Be 3
  3. Ce 4
  4. De 5

Correct answer

A. e 2

Step-by-step solution

We have n th term T_n= 1+2+3+ +n (n+1) ! = n(n+1) 2 (n+1) ! = 1 2(n-1) ! Put n=1,2,3, ₁= 1 2 1 0 ! , T₂= 1 2 1 1 ! , T₃= 1 2 1 3 ! T₁+T₂+T₃+ = 1 2 [1+1+ 1 2 ! + 1 3 ! + ]= e 2

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