The-coefficient-of-the-term-independent-of-x-in-the-expansion-of-x-1-x-2-3-x-1-3-1-x-1-x-x-1-2-10-is-

Question Number 115399 by EvoneAkashi last updated on 25/Sep/20

The coefficient of the term independent

of x in the expansion of

{(\frac{x + 1}{x^{2 / 3} - x^{1 / 3} + 1} - \frac{x - 1}{x - x^{1 / 2}})}^{10} is

Answered by Dwaipayan Shikari last updated on 25/Sep/20

{(\frac{x + 1}{(x + 1)} . (x^{\frac{1}{3}} + 1) - \frac{(x^{\frac{1}{2}} + 1) (x^{\frac{1}{2}} - 1)}{x^{\frac{1}{2}} (x^{\frac{1}{2}} - 1)})}^{10}

= {(x^{\frac{1}{3}} + 1 - 1 - x^{- \frac{1}{2}})}^{10}

= {(x^{\frac{1}{3}} - x^{- \frac{1}{2}})}^{10} = x^{- 5} {(x^{\frac{5}{6}} - 1)}^{10}

T_{r + 1} = x^{- 5} (\begin{matrix} 10 \\ r \end{matrix}) x^{\frac{5 r}{6}} {(- 1)}^{10 - r}

{(x)}^{\frac{5 r}{6}} = x^{5}

r = 6

T_{6 + 1} Coefficient = (\frac{10!}{6! 4!}) = 210

Commented by mr W last updated on 25/Sep/20

w h a t i f t h e q u e s t i o n i s

{(\frac{x + 1}{x^{2 / 3} - x^{1 / 3} + 1} - \frac{x - 1}{x - x^{1 / 2} + 1})}^{10}

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