You have, skipping over your second term which simply makes no sense,
[tex]\frac{e^n}{3^{n-1}}= \frac{1}{e}\left(\frac{e}{3}\right)^{n-1}[/tex]
which is wrong- you have factored and e out of the numerator: it should be
[tex]\frac{e^n}{3^{n-1}}= e\left(\frac{e}{3}\right)^{n-1}[/tex]