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Question: If (1 –x + x<sup>2</sup>)<sup>n</sup> = a<sub>0</sub> + a<sub>1</sub>x + a<sub>2</sub>x<sup>2</sup> ...

If (1 –x + x2)n = a0 + a1x + a2x2 ……..+a2nx2n then

a0 + a2 + a4 ………+ a2n=

A

3n+12\frac{3^{n} + 1}{2}

B

3n−12\frac{3^{n} - 1}{2}

C

3n−1+12\frac{3^{n - 1} + 1}{2}

D

None of these

Answer

3n+12\frac{3^{n} + 1}{2}

Explanation

Solution

(x=1)+(x=−1)2\frac{(x = 1) + (x = - 1)}{2}=1+3n2\frac{1 + 3^{n}}{2}