What is maclaurin (1+x)^{-5/2} ?

The answer to maclaurin (1+x)^{-5/2} is 1-5/2 x+35/8 x^2-105/16 x^3+1155/128 x^4+\ldots

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maclaurin (1+x)^{-5/2}

maclaurin

(1 + x)^{- \frac{5}{2}}

1 - \frac{5}{2} x + \frac{35}{8} x^{2} - \frac{105}{16} x^{3} + \frac{1155}{128} x^{4} + \dots

Solution steps

Apply the Maclaurin Formula

= 1 + \frac{\frac{d}{d x} ( ( 1 + x ) ^{- \frac{5}{2}} ) ( 0 )}{1 !} x + \frac{\frac{d ^{2}}{d x ^{2}} ( ( 1 + x ) ^{- \frac{5}{2}} ) ( 0 )}{2 !} x^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( ( 1 + x ) ^{- \frac{5}{2}} ) ( 0 )}{3 !} x^{3} + \dots

Evaluate Derivatives

= 1 + \frac{- \frac{5}{2}}{1 !} x + \frac{\frac{35}{4}}{2 !} x^{2} + \frac{- \frac{315}{8}}{3 !} x^{3} + \frac{\frac{3465}{16}}{4 !} x^{4} + \dots

Refine

= 1 - \frac{5}{2} x + \frac{35}{8} x^{2} - \frac{105}{16} x^{3} + \frac{1155}{128} x^{4} + \dots

What is maclaurin (1+x)^{-5/2} ?
The answer to maclaurin (1+x)^{-5/2} is 1-5/2 x+35/8 x^2-105/16 x^3+1155/128 x^4+\ldots