Sum of binomial co-efficients of (1+x+x^2)^n = 3^n. (As given in the book)

But if I expand (1+x+x^2)^n = [1+x(1+x)]^n and then put x = 1, am not getting 3^n. Somebody help.

Dear Palash Chatterjee,

You have overlooked your answer a bit !

Look ....by putting x=1 in [1+x(1+x)]ⁿ we really get 3ⁿ which is the answer required !!

It is [1+1(1+1)]ⁿ when we put x=1

=[1+2]ⁿ

=3ⁿ

Hope this made you clear..

All the Best & Good Luck !!

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Sagar Singh - IIT Delhi

I was actually making a mistake while expanding the equation (I messed up the co-efficients). Anyway, thanks a lot for y our help.