Let n be a positive integer and- 1-x n - a 0 - a 1 x- a 2 x 2 - - a n x n- What is a 0 - a 1 - a 2 - - a n equal to-

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Sum of Coefficients of All Terms

Let n be a ...

Question

Let $n$ be a positive integer and, ${(1 + x)}^{n} = a_{0} + a_{1} x + a_{2} x^{2} + \dots + a_{n} x^{n}$ . What is $a_{0} + a_{1} + a_{2} + \dots + a_{n}$ equal to?

1

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2^{n}

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2^{n - 1}

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2^{n + 1}

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\frac{1}{a_{0}} + \frac{x}{a_{0} a_{1}} + \frac{x^{2}}{a_{0} a_{1} a_{2}} + \dots + \frac{x^{n}}{a_{0} a_{1} a_{2} \dots a_{n}} = \frac{1}{a_{0} -} \frac{a_{0} x}{a_{1} + x -} \frac{a_{1} x}{a_{2} + x -} \dots \frac{a_{n - 1} x}{a_{n} + x}

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

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

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

A_{0}, A_{1}, A_{2}

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\frac{1}{\sqrt{4 x + 1}} [{(\frac{1 + \sqrt{4 x + 1}}{2})}^{n} - {(\frac{1 - \sqrt{4 x + 1}}{2})}^{n}] = a_{0} + a_{1} x + a_{2} x^{2} + . . . . + a_{5} x^{5}

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

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