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(1+x+x^2)^n=a0+a1x+a2x^2+a3x^3+...+a2nx^2n Prove that a0+a2+..+an=(1/2)*(3^n+an)

(1+x+x^2)^n=a0+a1x+a2x^2+a3x^3+...+a2nx^2n


Prove that a0+a2+..+an=(1/2)*(3^n+an)

Grade:11

4 Answers

NANDA
18 Points
8 years ago
(1+x+x^2)^n=a0+a1x+a2x^2+a3x^3+...+a2nx^2n put x=1 you get 3^n=a0+a1+a2 ....................a2n putx=-1 1^n=a0-a1+a2.........................a2n 3^n+1=2(a0+a2+a4+ ...... ....... a2n) a0+a2+a4+a6+......a2n=(3^n+1)/2
Shadow
16 Points
8 years ago
Lol you haven`t solved what he has asked for
Comfortably Numb
31 Points
8 years ago
Got the answer myself.
Rishi Sharma
askIITians Faculty 646 Points
one year ago
Dear Student,
Please find below in the attached image the solution to your problem.

Thanks and Regards
645-1190_WhatsApp Image 2020-07-10 at 2.54.52 AM.jpeg

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