What is maclaurin (1+x)^{1/4} ?

The answer to maclaurin (1+x)^{1/4} is 1+1/4 x-3/32 x^2+7/128 x^3-77/2048 x^4+\ldots

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maclaurin (1+x)^{1/4}

maclaurin

(1 + x)^{\frac{1}{4}}

1 + \frac{1}{4} x - \frac{3}{32} x^{2} + \frac{7}{128} x^{3} - \frac{77}{2048} x^{4} + \dots

Solution steps

Apply the Maclaurin Formula

= 1 + \frac{\frac{d}{d x} ( ( 1 + x ) ^{\frac{1}{4}} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( ( 1 + x ) ^{\frac{1}{4}} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( ( 1 + x ) ^{\frac{1}{4}} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{\frac{1}{4}}{1 !} x + \frac{- \frac{3}{16}}{2 !} x^{2} + \frac{\frac{21}{64}}{3 !} x^{3} + \frac{- \frac{231}{256}}{4 !} x^{4} + \dots

Refine

= 1 + \frac{1}{4} x - \frac{3}{32} x^{2} + \frac{7}{128} x^{3} - \frac{77}{2048} x^{4} + \dots

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What is maclaurin (1+x)^{1/4} ?
The answer to maclaurin (1+x)^{1/4} is 1+1/4 x-3/32 x^2+7/128 x^3-77/2048 x^4+\ldots