What is taylor 1/((7+x)^2) ?

The answer to taylor 1/((7+x)^2) is 1/49-2/343 x+3/2401 x^2-4/16807 x^3+5/117649 x^4+\ldots

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taylor 1/((7+x)^2)

taylor

\frac{1}{( 7 + x ) ^{2}}

\frac{1}{49} - \frac{2}{343} x + \frac{3}{2401} x^{2} - \frac{4}{16807} x^{3} + \frac{5}{117649} x^{4} + \dots

Solution steps

Apply the Taylor Formula

= \frac{1}{49} + \frac{\frac{d}{d x} ( \frac{1}{( 7 + x ) ^{2}} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{1}{( 7 + x ) ^{2}} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{1}{( 7 + x ) ^{2}} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= \frac{1}{49} + \frac{- \frac{2}{343}}{1 !} x + \frac{\frac{6}{2401}}{2 !} x^{2} + \frac{- \frac{24}{16807}}{3 !} x^{3} + \frac{\frac{120}{117649}}{4 !} x^{4} + \dots

Refine

= \frac{1}{49} - \frac{2}{343} x + \frac{3}{2401} x^{2} - \frac{4}{16807} x^{3} + \frac{5}{117649} x^{4} + \dots

y = \frac{4 x}{x ^{2} + 1}, (1, 2)

\int 2 + t d t

x \to \infty lim (x^{- 2} e^{2 x})

What is taylor 1/((7+x)^2) ?
The answer to taylor 1/((7+x)^2) is 1/49-2/343 x+3/2401 x^2-4/16807 x^3+5/117649 x^4+\ldots