Question

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??

Answer 1

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`