What is taylor ((1-v))/((1+v)) ?

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

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taylor ((1-v))/((1+v))

taylor

\frac{( 1 - v )}{( 1 + v )}

1 - 2 v + 2 v^{2} - 2 v^{3} + 2 v^{4} + \dots

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{- 2}{1 !} v + \frac{4}{2 !} v^{2} + \frac{- 12}{3 !} v^{3} + \frac{48}{4 !} v^{4} + \dots

Refine

= 1 - 2 v + 2 v^{2} - 2 v^{3} + 2 v^{4} + \dots

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