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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.

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. 

Grade:12

3 Answers

Godfrey Classic Prince
633 Points
12 years ago

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 !!

Please approve my answer if you liked it by clicking on "Yes" given below...!!Smile

SAGAR SINGH - IIT DELHI
878 Points
12 years ago

Dear student,

You are making error in bracket term while taking common...

BEST OF LUCK..!!!!


 

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Sagar Singh - IIT Delhi

Palash Chatterjee
14 Points
12 years ago

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

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