What is maclaurin 1/(1-t) ?

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

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maclaurin 1/(1-t)

maclaurin

\frac{1}{1 - t}

Solution steps

Apply the Maclaurin Formula

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

Evaluate Derivatives

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

Refine

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

The series sum representation

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

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