What is taylor (1-x)^{-100} ?

The answer to taylor (1-x)^{-100} is 1+100x+5050x^2+171700x^3+4421275x^4+\ldots

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taylor (1-x)^{-100}

taylor

(1 - x)^{- 100}

1 + 100 x + 5050 x^{2} + 171700 x^{3} + 4421275 x^{4} + \dots

Solution steps

Apply the Taylor Formula

= 1 + \frac{\frac{d}{d x} ( ( 1 - x ) ^{- 100} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( ( 1 - x ) ^{- 100} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( ( 1 - x ) ^{- 100} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{100}{1 !} x + \frac{10100}{2 !} x^{2} + \frac{1030200}{3 !} x^{3} + \frac{106110600}{4 !} x^{4} + \dots

Refine

= 1 + 100 x + 5050 x^{2} + 171700 x^{3} + 4421275 x^{4} + \dots

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T \to \infty lim (f (T))

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\frac{x}{y}

What is taylor (1-x)^{-100} ?
The answer to taylor (1-x)^{-100} is 1+100x+5050x^2+171700x^3+4421275x^4+\ldots