What is taylor 1/(1-1/x),0 ?

The answer to taylor 1/(1-1/x),0 is -x-x^2-x^3-x^4-x^5+\ldots

Popular >

taylor 1/(1-1/x),0

taylor

\frac{1}{1 - \frac{1}{x}}, 0

- x - x^{2} - x^{3} - x^{4} - x^{5} + \dots

Solution steps

Apply the Taylor Formula

= 0 + \frac{\frac{d}{d x} ( \frac{1}{1 - \frac{1}{x}} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{1}{1 - \frac{1}{x}} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{1}{1 - \frac{1}{x}} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 0 + \frac{- 1}{1 !} x + \frac{- 2}{2 !} x^{2} + \frac{- 6}{3 !} x^{3} + \frac{- 24}{4 !} x^{4} + \frac{- 120}{5 !} x^{5} + \dots

Refine

= - x - x^{2} - x^{3} - x^{4} - x^{5} + \dots

\int \frac{1}{( b ^{2} - x ^{2} ) ^{\frac{3}{2}}} d x

f (x) = 10 x^{2} + 10 x + 8 + ln (x)

y^{^{''}} + 9 y = cos (6 t)

x \to 2 - lim (2)

y = arctan (- 2 x), at x = - 3

What is taylor 1/(1-1/x),0 ?
The answer to taylor 1/(1-1/x),0 is -x-x^2-x^3-x^4-x^5+\ldots