Geometric series sum $\sum_2^\infty e^{3-2n}$ $$\sum_2^\infty e^{3-2n}$$
The formulas for these things are so ambiguous I really have no clue on how to use them.
$$\frac {cr^M}{1-r}$$
$$\frac {1e^2}{1-\frac{1}{e}}$$
Is that a wrong application of the formula and why?

For me, it is most helpful to write out the first few terms of the series:
$$\sum_{n=2}^{\infty}e^{3-2n}=e^{-1}+e^{-3}+e^{-5}+\ldots$$
From this, it is easy to see that the initial term of the series is $a=e^{-1}$, and the common ratio is $r=e^{-2}$.  Using the formula for an infinite geometric series we have:
$$S=\frac{a}{1-r}=\frac{e^{-1}}{1-e^{-2}}=\frac{e}{e^2-1}$$
