What is taylor 1/(1-y) ?

The answer to taylor 1/(1-y) is sum from n=0 to infinity of x^n

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taylor 1/(1-y)

taylor

\frac{1}{1 - y}

n = 0 \sum \infty x^{n}

Solution steps

Apply the Taylor Formula

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

Evaluate Derivatives

= 1 + \frac{1}{1 !} y + \frac{2}{2 !} y^{2} + \frac{6}{3 !} y^{3} + \frac{24}{4 !} y^{4} + \dots

Refine

= 1 + y + y^{2} + y^{3} + y^{4} + \dots

The series sum representation

= n = 0 \sum \infty x^{n}

\frac{d}{d x} (3 x^{2} cos (x) cot (x))

x = 6 y^{2}, x = 16 + 2 y^{2}

x \to - \infty lim (\frac{5 x ^{2} - sin ( 3 x )}{x ^{2} + 10})

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

\frac{d}{d x} (tan (5 - sin (2 x)))

What is taylor 1/(1-y) ?
The answer to taylor 1/(1-y) is sum from n=0 to infinity of x^n