Find the coefficient of x in the expansion of (2x-1/x)^5. I used nCr (a)^n-r (b)^r.but I'm not getting coefficient in terms of x??

1 Answer
Mar 11, 2018

The coefficient is #-80#

Explanation:

In the expansion of #(2x-1/x)^5#, #(r+1)^(th)# term will be

#C_r^5(2x)^(5-r)(-1/x)^r#

or #C_r^5 2^(5-r)(-1)^rxx x^(5-r)/x^r#

or #C_r^5 2^(5-r)(-1)^rxx x^(5-2r)#

For coefficient of #x#, the power of #x# needs to be #1#

therefore #5-2r=1# i.e. #r=2#

and the term is #C_2^5 2^3(-1)^3x#

= #-(5xx4)/(1xx2)xx8x=-80x#

and coefficient is #-80#