If 1-x-x2n-a0-a1 x-a2 x2-a2 n x2 n- then a0-a2-a4-a2 n equalsa 3 n-12b 3 n-12c 1-3 n 2d 3 n-12

Given: (1 #160; #8211; #160;x #160;+ #160;x2)n #160;= #160;a0 #160;+ #160;a1 #160;x #160;+ #160;a2 #160;x2 #160;+ #160;....+a2n ...

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Equation

If 1-x+x2n=a0...

Question

If (1 – x + x²)ⁿ = a₀ + a₁ x + a₂ x² +...+a_2n x²ⁿ, then a₀ + a₂ + a₄ +...+ a_2n equals

(a) $\frac{3^{n} + 1}{2}$

(b) $\frac{3^{n} - 1}{2}$

(c) $\frac{1 - 3^{n}}{2}$

(d) $3^{n} + \frac{1}{2}$

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(1 - x + x^{2})^{n} = a_{0} + a_{1} x + a_{2} x^{2} + . . . . + a_{2 n} x^{2 n}

a_{0} + a_{2} + a_{4} + . . . . + a_{2 n}

(1 + x + x^{2})^{n} = a_{0} + a_{1} x + a_{2} x^{2} + . . . + a_{2 n} x^{2 n}

E_{1} = a_{0} + a_{3} + a_{6} + . . .

E_{2} = a_{1} + a_{4} + a_{7} + . . .

E_{3} = a_{2} + a_{5} + a_{8} + . . .

{(1 - x + x^{2})}^{n} = a_{0} + a_{1} x + a_{2} x^{2} + . . . + a_{2 n} x^{2 n}

a_{0} + a_{2} + a_{4} + . . . + a_{2 n}

(1 + x + x^{2})^{n}

a_{0} + a_{1} x + a_{2} x^{2} + . . . . . + a_{r} x^{r} + . . . . . + a_{2 n} x^{2 n}

a_{0} + a_{3} + a_{6} + . . . . . = a_{1} + a_{4} + a_{7} + . . . . . = a_{2} + a_{5} + a_{8} + . . . . = 3^{n - 1}

(1 + x + x^{2}) n = a 0 + a^{1} x + a^{2} x + a^{3} x^{3} + . . . . . . . a (2^{n}) x (2^{n})

(a^{0} + a^{3} + a^{6} + . . . . . . . . .) = (a^{1} + a^{4} + a^{7}) = (a^{2} + a^{5} + a^{8}) = 3^{(} n - 1),

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