Question

Find the
$\sf {8}^{th} \: term \: of \bigg(1 - \dfrac{5x}{2} \bigg) ^{ \frac{ - 3}{5} }$
​

Answer 1

$\sf {8}^{th} \: term \: of \bigg(1 - \dfrac{5x}{2} \bigg) ^{ \dfrac{ - 3}{5} }$

$\underline{ \underline{ \sf{ \red{sol.}}}} \red{ :} \rm{On \: comparing \: with \: (1-X)^ \dfrac{-p}{q}, \: we \: get}$

$\rm{X = \dfrac{5x}{2}, \: p = 3, \: q=5}$

$\rm{The \: general \: term \: in \: this \: expansion \: is}$

$\boxed{ \boxed{T_{r+1}= \dfrac{p(p+q)...(p+(r-1)q)}{r!} \bigg( \dfrac{X}{q} \bigg)^r}}$

$\rm{Put \: r = 7, \: we \: get }$

$\implies \: T_{7+1}= \dfrac{3(3+5)...(3+(7-1)5)}{7!} \bigg( \dfrac{5x}{10} \bigg)^7$

$\boxed{ \boxed{ \rm{T_8 = \dfrac{3(8)(13)...(33)}{7!} \bigg( \dfrac{x}{2} \bigg)^7}}}$