If 1-x-x2n - -r-02n arxr- then a1-2a2-3a3- - -2n-a2n - -

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Chain Rule of Differentiation

If 1+x+x2n ...

Question

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

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Solution

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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} . . . . - 2 n a_{2 n}

(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

{(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}

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} + \cdot \cdot + x^{n})}^{n}

= a_{0} + a_{1} x + a_{2} x^{2} + \cdot \cdot \cdot + a_{m p} x^{m p}

a_{1} + 2 a_{2} + 3 a_{3} + \cdot \cdot \cdot + n p a_{n p}

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