Show that the expansion of (x^2+1/x)^12 does not contain any term involving x^-1 .

Question

Show that the expansion of \(\Big(x^2+\frac{1}{x}\Big)^{12}\) does not contain any term involving x^-1 .

Answer 1

For ,  \(\Big(x^2+\frac{1}{x}\Big)^{12}\) 

a = x² ,b = \(\frac{1}{x}\) and n=12 

We have a formula,

To get coefficient of x^-1 we must have,

(x)^24-3r = (x)^-1 

• 24 - 3r = -1 

• 3r = 25 

• r = 8.3333

As (²⁰_r) = (²⁰_8.3333) is not possible 

Therefore, the term containing x^-1 does not exist in the expansion of \(\Big(x^2+\frac{1}{x}\Big)^{12}\)