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BITSAT2011MathematicsBinomial TheoremActual

For (n N , x^ n+1 +(x+1)^ 2 n-1 ) is divisible by

Options

  1. A(x )
  2. B(x+1 )
  3. C(x^2+x+1 )
  4. D(x^2-x+1 )

Correct answer

C. (x^2+x+1 )

Step-by-step solution

For (n=1 ), we have; (x^ n+1 +(x+1)^ 2 n-1 =x^2+(x+1)=x^2+x+1 , ) which is divisible by (x^2+x+1 ) For (n=2 ), we have; (x^ n+1 +(x+1)^ 2 n-1 ) (=x^3+(x+1)^3=(2 x+1) (x^2+x+1 ) , ) which is divisible by (x^2+x+1 ).

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