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AP EAMCET20227 Jul 2022Morning ShiftMathematicsBinomial TheoremActual

What is the sum of the first n -terms of the series, whose k -term is k ! k ?

Options

  1. A(n+1) !^n-1
  2. B(n+1)^n-1
  3. C(n+1) !-1
  4. D3 n-2

Correct answer

C. (n+1) !-1

Step-by-step solution

Given, aligned t_k & =k k !=(k+1-1) k ! & =(k+1) k !-k !=(k+1) !-k ! aligned aligned & t₁=2 !-1 ! & t₂=3 !-2 ! & t₃=4 !-3 ! aligned ......... ......... t_n=(n+1) !-n ! t₁+t₂+ .+t_n=(n+1) !-1 Required sum =(n+1) !-1

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