Question

expansion of 1/1-x in ascending powers of X is​

Answer 1

Answer:

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Answer 2

To find: expansion of  $\frac{1}{1-x}$

Explanation

here we use the binomial expansion Formula.

we can write

$\frac{1}{1-x} = (1-x)^{-1}$

now we know that,

According to binomial expansion,

[tex](1+x)^{n} = 1+nx+\frac{n(n-1)}{2!}x^{2} +\frac{n(n-1)(n-2)}{3!}x^{3}+...\\ [/tex]     ----(1)

here, according to question

n = -1 and x=-x

putting the value in equation (1)

[tex](1-x)^{-1} = 1-(-1)x+\frac{(-1)(-1-1)}{2!}x^{2} +\frac{(-1)(-1-1)(-1-2)}{3!}x^{3}+...\\\\ \\ (1-x)^{-1} = 1+x+\frac{(-1)(-2)}{2!}x^{2} +\frac{(-1)(-2)(-3)}{3!}x^{3}+... \\\\\\ (1-x)^{-1} = 1+x+x^{2} +x^{3}+....[/tex]

(Here 3! = 3×2×1 and 2! = 2×1)

Therefore, the expansion of 1/(1-x) is 1 + x + x² + x³ +...

Binomial Expansion = It is the algebric expression with two terms.

Binomial expansion formulas are used to find powers of binomials that cannot be found with the help of algebraic identities.