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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
10 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
10 years ago
Lol you haven`t solved what he has asked for
Comfortably Numb
31 Points
10 years ago
Got the answer myself.
Rishi Sharma
askIITians Faculty 646 Points
3 years 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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