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KCET2009MathematicsBinomial Theorem

If f ( x )=1+ nx + n ( n -1) 2 x ²+ n(n-1)(n-2) 6 x³+ +x^ n then f ^ (1) is equal to

Options

  1. An ( n -1) 2^ n -1
  2. B(n-1) 2^ n-1
  3. Cn(n-1) 2^ n-2
  4. Dn(n-1) 2^ n

Correct answer

C. n(n-1) 2^ n-2

Step-by-step solution

Given, f ( x )=1+ nx + n ( n -1) 2 ! x ²+ n ( n -1)( n -2) 3 ! x ³+ + x ^ n array ll & f ( x )=(1+ x )^ n & f ^ ( x )= n (1+ x )^ n -1 & f ^ ( x )= n ( n -1)(1+ x )^ n -2 & f ^ (1)= n ( n -1) 2^ n -2 array

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