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Manipal MET2010MathematicsBinomial Theorem

The constant term in the expansion of (1+x)^m (1+ 1 x )^n is

Options

  1. Am+n m-1
  2. B^ m+n C_n
  3. Cm+n m-n
  4. DNone of these

Correct answer

B. ^ m+n C_n

Step-by-step solution

We have, (1+x)^m (1+ 1 x )^n=(1+x)^m ( x+1 x )^n= (1+x)^ m+n x^n =x^ -n (1+x)^ m+n Required term independent of x= Coefficient of x^0 in x^ -n (1+x)^ m+n = Coefficient of x^n in (1+x)^ m+n = ^ m+n C_n

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