Limits of series. I am going to type the equation using equation editor.

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions.

A community for students.

Limits of series. I am going to type the equation using equation editor.

Mathematics
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions

I am trying to find the following limit. \[\lim_{n \rightarrow \inf} \frac{ 2(n!) }{ (-6)^n }\]
Factorial will grow much much bigger than any exponential growth (after some point).
Is it because the factorial is multiplied by 2?

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

I was under the assumption that the (-6)^n would grow faster than the factorial.
two does not do anything at all.... whether it has a two or not factorial is much bigger. Wrong assumption! The opposite is true
Then I guess the limit diverges to both negative and positive infinity.
Yes:) positive and negative infinity, because it alternates.
Alright, Thanks. I guess my understand of factorials are a bit off.
We can play around and maybe apply Stirling's approximation: (Note, that the factorial is greater than its stirlings approximation) \(\large\color{black}{ \displaystyle n!\approx\frac{\sqrt{2\pi n}{~}n^n}{e^n} }\) \(\large\color{black}{ \displaystyle \frac{n!}{6^n}\approx\frac{\sqrt{2\pi n}{~}n^n}{6^ne^n} }\) \(\large\color{black}{ \displaystyle \frac{n!}{6^n}\approx\sqrt{2\pi n}\frac{{~}n^n}{(6e)^n} }\)
thx i learned something new just by watching lol
You would then agree that the numerator is greater, right?
I do agree that the numerator is greater.
Good:) And I understand that you were applying the Diverghence test to \(\large\color{black}{ \displaystyle \sum_{ n=1 }^{ \infty } ~ \frac{2(n!)}{(-6)^n}}\)
(not necessarily n=1, but that series)
yep
Ok, so if it was the other way around, then you would apply: \(\large\color{black}{ \displaystyle \sum_{ n=0 }^{ \infty } ~ \frac{x^n}{n!}=e^x}\) So for example: \(\large\color{black}{ \displaystyle \sum_{ n=0 }^{ \infty } ~ \frac{(-6)^n}{n!}=e^{-6}= 1/e^6}\)
Anyway, good luck....
Thanks for the help. It really made since. I am now making forward progress on my assignments.
Good to hear that:)
be well

Not the answer you are looking for?

Search for more explanations.

Ask your own question