A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

why 2n+1/n+1 for n=infinity the answer is 2?

  • This Question is Closed
  1. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I'm assuming you are asking why, \[\lim_{n \rightarrow \infty} \frac{2n+1}{n+1} = 2\] Correct? Since both the numerator and denominator go to \(\infty\) in the limit you can do L'Hopital's Rule to prove this limit. Recall that in this case this simply means taking the derivative of the numerator and denominator and the taking the limit of the result. So, \[\lim_{n \rightarrow \infty} \frac{2n+1}{n+1}=\lim_{n \rightarrow \infty} \frac{2}{1} = 2\]

  2. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Another way to look at it is graphing (2x + 1)/(x + 1) and look at what happens when x is really big. Another way to think about it is to split up the fraction. (2n + 1)/(n+1) = (2n)/(n+1) + (1)/(n + 1). Taking the limit of both sides as n goes to infinity, we see that (n)/(n+1) approaches 1 as n goes to infinity, so (2n)/(n+1) approaches 2 as n goes to infinity. Also, 1/(n+1) approaches 0 as n goes to infinity. So (2n)/(n+1) + (1)/(n+1) approaches 2 + 0, or 2, as n goes to infinity.

  3. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.