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KVPY2011MathematicsBinomial Theorem

If f(x)=(2011+x)^ n , where x is a real variable and n is a positive integer, then the value of f(0)+f^ (0)+ f^ (0) 2 ! + .+ f^ (n-1) (0) (n-1) ! is -

Options

  1. A(2011)^ n
  2. B(2012)^ n
  3. C(2012)^ n -1
  4. Dn(2011)^ n

Correct answer

C. (2012)^ n -1

Step-by-step solution

(2011)^ n + ^ n C ₁(2011)^ n-1 + n 2 (2011)^ n-2 + + n n-1 2011+ n n-1 =(2011+1)^ n -1

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