What is taylor 1/(x^2) ?

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

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taylor 1/(x^2)

taylor

\frac{1}{x ^{2}}

1 - 2 (x - 1) + 3 (x - 1)^{2} - 4 (x - 1)^{3} + 5 (x - 1)^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

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

Refine

= 1 - 2 (x - 1) + 3 (x - 1)^{2} - 4 (x - 1)^{3} + 5 (x - 1)^{4} + \dots

\frac{d}{d x} (x^{3} - 21 x^{2} + 144 x)

\frac{d}{d x} (6^{3 x - 4})

\int_{0}^{x} sin (\frac{π}{2} t^{2}) d t

\frac{d}{d x} (2^{x} - x^{2})

\int_{0}^{1} x^{2} - x d x

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