Show that the coefficient of x^-3 in the expansion of (x - 1/x)^{11} is -330 ​

Question

Show that the coefficient of x^-3 in the expansion of \((x - \frac{1}x)^{11}\) is -330.

Answer 1

To Show: that the coefficient of x^-3 in the expansion of \((x - \frac{1}x)^{11}\)is -330

Formula Used: General term, T_r+1 of binomial expansion 9x + y)ⁿ is given by,

Now, finding the general term of the expression, \((x - \frac{1}x)^{11}\), we get

For finding the term which has x^-3 in it , is given by 

11 – 2r = 3 

2r = 14 

R = 7 

Thus, the term which the term which has x^-3 in it isT₈

Thus, the coefficient of x^-3 in the expansion of \((x - \frac{1}x)^{11}\)is -330