find the sum of coefficient of binomial expansion of (1+x+x^2)^6

The series (1+x+x²) represent geometric series with the first term a=1, common ratio r= x and the number of terms n=3. Its sum S_n=(a(1-rⁿ))/(1-r)=(1)(1-x²)/(1-x)=((1-x)(1+x))/(1-x)=(1+x).

Then the sum of (1+x+x²)⁶=(1+x)⁶.