First five terms of the sequence $a_n=2/e^n$ I just wanted to check  if my answer here is correct. I am not sure if I am supposed to simplify (e) even further down, and turn the fraction into a decimal or not because it does mention use exponents.

Find first five terms of the sequence $a_n=\dfrac{2}{e^n}$.


 A: Looks good to me. As for worrying about weather $n$ is a natural number or rational number, I wouldn't. Unless otherwise stated, (I believe) it is always assumed that a sequence is a map from the naturals to some other set. Hence, you are correct in evaluating the first five terms of your sequence as $$\frac{2}{e}, \frac{2}{e^2}, \dots ,\frac{2}{e^5}$$ The terms of the sequence cannot be simplified further because $e^n$ is irrational for integers $n>0$, so you can either leave your answer with the exponent in the denominator, or flip it up the numerator but change the exponent to be negative. However, the directions on the page you provided a link to specify to leave your answer with positive exponent only, so I wouldn't make the change.
A: First, when studying a series, you have to determine its domain. It's the same concept for functions, you don't want your series to take forbidden values.
Look at $f(n)$ : it is defined on $\mathbb{N}$ because the exponential only takes positive values. Once you've determined this, you can now enumerate the terms of your series.
And you did it successfully! 
Comment: you can write your result $2*e^{-2}$ and so on.
Best of luck.
