The sum of the coefficients in the expansion of $\left(1+x+x^2\right)^n$ is

The sum of the coefficients in the expansion of $\left(1+x+x^2\right)^n$ is
  1. $1$
  2. $2^n$
  3. $3^n$
  4. $4^n$

Solution

We have, $\left(1+x+x^2\right)^n$ Put $ \begin{aligned} x & =1 \\ & =\left(1+1+1^2\right)^n=3^n \end{aligned} $

Asked in: AP EAMCET 2002

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