"Binomial expansion of (1−x)n Weve" was answered by our experts

Ernest Ryland

Answered question

2021-12-14

Binomial expansion of

{(1 - x)}^{n}

Weve

Answer & Explanation

Deufemiak7

Beginner2021-12-15Added 34 answers

Well, as I understand it, we could write the binomial expansion as:

(1 - x)^{n} = \sum_{k = 0}^{n} (\begin{matrix} n \\ k \end{matrix}) 1^{n - k} (- x)^{k}

(\begin{matrix} n \\ 0 \end{matrix}) 1^{n} (- x)^{0} + (\begin{matrix} n \\ 1 \end{matrix}) 1^{n - 1} (- x) + (\begin{matrix} n \\ 2 \end{matrix}) 1^{n - 2} (- x)^{2} + (\begin{matrix} n \\ 3 \end{matrix}) 1^{n - 3} (- x)^{3} . . .

which simplifies to

1 - n x + \frac{n (n - 1)}{2!} \cdot x^{2} - \frac{n (n - 1) (n - 2)}{3!} \cdot x^{3} \dots

Which is the answer everyone else has given.

maul124uk

Beginner2021-12-16Added 35 answers

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