If 1-X-X2n-r-02narxr then- a1-2a2-3a3-2na2n is equal to

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Addition of Polynomials

If 1+X+X2n=...

Question

If $(1 + X + X^{2})^{n} = \sum_{r = 0}^{2 n} a_{r} x^{r}$ then, $a_{1} - 2 a_{2} + 3 a_{3} . . . . - 2 n a_{2 n}$ is equal to

n

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Similar questions

(1 + x + x^{2})^{n} = \sum_{r = 0}^{2 n} a_{r} x^{r}

a_{1} - 2 a_{2} + 3 a_{3} - \dots \dots - 2 n . a_{2 n} = \dots

(1 + x + x^{2})^{n} = 2 n \sum r = 0 a_{r} x^{r}

a_{1} - 2 a_{2} + 3 a_{3} - \dots . - 2 n a_{2 n} = \dots

a_{k}

x^{k}

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

k = 0, 1, 2,

\dots

2 n

a_{1} + 2 a_{2} + 3 a_{3} + \dots + 2 n a_{2_{n}} =

{(1 + x + x^{2})}^{n} = 2 n \sum r = 0 a_{r} x^{r}

a_{0} + a_{1} + a_{2} + a_{3} \dots a_{n - 1}

n

{(1 + x + x^{2})}^{n} = n \sum r = 0 a_{r} x^{r}

(0 ⩽ r ⩽ 2 n)

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