By considering the general term in the binomial expansion of $\left(x^2 - \frac{1}{2x}\right)^{17}$, explain why there is no independent term in this expansion.

1. Write down the general term of the binomial expansion

The general term is given by:
$T_{r+1} = \binom{17}{r} (x^2)^{17-r} \left(-\frac{1}{2x}\right)^r$

2. Simplify the general term to isolate the power of $x$

$T_{r+1} = \binom{17}{r} x^{34-2r} \left(-\frac{1}{2}\right)^r x^{-r}$
$T_{r+1} = \binom{17}{r} \left(-\frac{1}{2}\right)^r x^{34-3r}$

3. Equate the power of $x$ to 0 and solve for $r$

For the term independent of $x$, the power of $x$ must be 0:
$34 - 3r = 0$
$3r = 34$
$r = \frac{34}{3} = 11\frac{1}{3}$

4. Explain why there is no independent term

Since $r$ must be an integer ($0 \leqslant r \leqslant 17$) and $11\frac{1}{3}$ is not an integer, there is no term independent of $x$ in the expansion.