As a complement to Matt's answer, on the intuition: $u[n]$ has value $1$ from $n=0$ on. So basically its energy will increase for ever, because it keeps adding ones for $n\ge0$. Then, you build another signal $x[n]$ that grows way faster because you multiply it with the exponential term $4^n$. 

Therefore, only at the common sense level, one cannot expect it to be an energy signal. It is not feasible. 

And then, goes the proof that the sum of the series actually diverges.