find-the-term-independent-of-x-in-x-1-x-9-

Question Number 78160 by Lontum Hans last updated on 14/Jan/20

find the term independent of x in

{[\frac{x - 1}{x}]}^{9}

Commented by mathmax by abdo last updated on 14/Jan/20

{(\frac{x - 1}{x})}^{9} = {(1 - \frac{1}{x})}^{9} = - {(\frac{1}{x} - 1)}^{9} = - \sum_{k = 0}^{9} C_{9}^{k} {(\frac{1}{x})}^{k} {(- 1)}^{9 - k}

= - \sum_{k = 0}^{9} \frac{C_{9}^{k}}{x^{k}} w e g e t t h e i n d e p e n d a n t t e r m o f x f o r k = 0 \Rightarrow

a_{0} = - C_{9}^{0} {(- 1)}^{9} = 1