To Find : term independent of x, i.e. coefficient of x0
Formula: tr+1 = (rn) an-rbr
We have a formula,
tr+1 = (rn) an-rbr
Therefore, the expansion of \(\Big(x-\frac{2}{x}\Big)^{10}\) is given by,
Multiplying the second bracket by 91, x and 2x3
In the first bracket, there will be a 6th term of x0 having coefficient 91 (-2)5(510)
While in the second and third bracket, the constant term is absent.
Therefore, the coefficient of term independent of x, i.e. constant term in the above expansion
= 91 (-2)5(510)
= 91(-2)5 \(\frac{10\times9\times8\times7\times6}{5\times4\times3\times2\times1}\)
= – 91(2)5 (252)
Conclusion: coefficient of term independent of x =-91(2)5 (252)