What is taylor 1/(1-x),7 ?

The answer to taylor 1/(1-x),7 is -1/6+1/36 (x-7)-1/216 (x-7)^2+1/1296 (x-7)^3-1/7776 (x-7)^4+\ldots

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taylor 1/(1-x),7

taylor

\frac{1}{1 - x}, 7

- \frac{1}{6} + \frac{1}{36} (x - 7) - \frac{1}{216} (x - 7)^{2} + \frac{1}{1296} (x - 7)^{3} - \frac{1}{7776} (x - 7)^{4} + \dots

Solution steps

Apply the Taylor Formula

= - \frac{1}{6} + \frac{\frac{d}{d x} ( \frac{1}{1 - x} ) ( 7 )}{1 !} (x - 7) + \frac{\frac{d ^{2}}{d x ^{2}} ( \frac{1}{1 - x} ) ( 7 )}{2 !} (x - 7)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( \frac{1}{1 - x} ) ( 7 )}{3 !} (x - 7)^{3} + \dots

Evaluate Derivatives

= - \frac{1}{6} + \frac{\frac{1}{36}}{1 !} (x - 7) + \frac{- \frac{1}{108}}{2 !} (x - 7)^{2} + \frac{\frac{1}{216}}{3 !} (x - 7)^{3} + \frac{- \frac{1}{324}}{4 !} (x - 7)^{4} + \dots

Refine

= - \frac{1}{6} + \frac{1}{36} (x - 7) - \frac{1}{216} (x - 7)^{2} + \frac{1}{1296} (x - 7)^{3} - \frac{1}{7776} (x - 7)^{4} + \dots

What is taylor 1/(1-x),7 ?
The answer to taylor 1/(1-x),7 is -1/6+1/36 (x-7)-1/216 (x-7)^2+1/1296 (x-7)^3-1/7776 (x-7)^4+\ldots