Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.)
An=(n^2)(e^-n)
by this time you should know that exponentials always overcome polynomials.
To determine whether the sequence converges or diverges, we can find the limit of the sequence as n approaches infinity.
First, let's calculate the limit of the sequence by finding the limit of the expression (n^2)(e^-n) as n approaches infinity.
lim(n→∞) (n^2)(e^-n)
To simplify the expression, we can use the fact that the limit of e^-n as n approaches infinity is 0.
lim(n→∞) (n^2)(e^-n) = lim(n→∞) (n^2)(0)
Since anything multiplied by 0 is 0, we can conclude that the limit of the sequence An = (n^2)(e^-n) as n approaches infinity is 0.
Therefore, the sequence converges to 0.