Find the term independent of $x$ in the expansion of the expression ${(2 x - \frac{1}{x})}^{10}$ .

Open in App

Solution

We have,
${(2 x - \frac{1}{x})}^{10}$

The term independent of $x$ index of the means index of the term should be zero.
The first we will find the general term.

$T_{r + 1} =^{10} C_{r} (2 x)^{10 - r} (- \frac{1}{x})^{r}$

Solve this and we will get index of $x = 10 - 2 r$

Put $10 - 2 r = 0$
$r = 5$

if $r = 5$ , then term will be $6 t h$
Put $r = 5$ in the general term, we will get
$T_{6} = - 4032$

Hence, this is the answer.

Suggest Corrections

Similar questions

x

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

x

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

x

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

x

{(1 - x)}^{2}

{(x + \frac{1}{x})}^{10}

(i) Find the value of r, if the coefficients of (2r + 2)th and (r-2)th terms in the expansion of (1+x)^{18} are equal.

(ii) Find the coefficient of $x^{-} 17$ in the expansion of ${(x^{4} - \frac{1}{x^{3}})}^{15}$

(iii) Find the term independent of x in the expansion of ${(2 x - \frac{1}{x})}^{10}$

Join BYJU'S Learning Program