Careful! You can't cancel the n's here since n is not a factor of either the numerator, nor the denominator.

What you can do is this. Divide both the numerator and denominator by n:

$\displaystyle \left | \frac{4n+2}{2n+1} \right | = \left | \frac{4 + \frac{2}{n}}{2 + \frac{1}{n}} \right |$

Now, since n is large this is approximately:

$\displaystyle \left | \frac{4n+2}{2n+1} \right | = \left | \frac{4 + \frac{2}{n}}{2 + \frac{1}{n}} \right | \approx \left | \frac{4}{2} \right | = 2$

Which shows that the series diverges.

-Dan