Find the constant term in expansion (x-1/x )^10

Question

Find the constant term in expansion \((x-\frac{1}{x})^{10}\) 

Answer 1

 T_{r + 1} = ¹⁰Cr (x)^{10 – r} \((\frac{-1}{x})^r\)

= ¹⁰Cr (x)^{10 – 2r} (– 1)^r 

= (– 1)^{r 10} Cr x^10-2r

For the constant term, put 10 – 2r = 0 

We get, r = 5 

Hence, T^{5 + 1} = T₆ i.e^th term of the expansion is constant. 

T₆ = T_{5 + 1} = ¹⁰C₅ (– 1)5 x^{10 – 10}

= -252