Determine the coefficient of $x^{18}$ in $\left(x+\frac{1}{x}\right)^{50}$ 
Determine the coefficient of $x^{18}$ in $\left(x+\frac{1}{x}\right)^{50}$.

I know he Binomial Theorem will be useful here, but I am struggling to use it with any certainty.

Hint The general term of the binomial expansion is $${50 \choose k} x^k \left(\frac{1}{x}\right)^{50 - k} = {50 \choose k} x^{2k - 50} .$$
