1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Finding the limit of a sequence

  1. Aug 17, 2014 #1
    1. The problem statement, all variables and given/known data

    How do you determine if the limit of (1+1/n^2)^(n^2) exists and what it is?
    This cannot use logarithms at any point.

    2. Relevant equations
    (1+1/n)^n --> e

    3. The attempt at a solution

    Let N=n^2
    Given (1+1/N)^N --> e, then (1+1/n^2)^(n^2) must --> e also.
    Is this allowed though? Do I need to put restrictions on N?
    I was thinking that I might need to show that N and n^2 have the same limit on their own, but since I have created N, it's limit is obviously that of n^2.
  2. jcsd
  3. Aug 17, 2014 #2

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper

    Which limit do you mean?
    ... I cannot tell what the person marking you work will or will not allow. It is OK mathematically - except you need the "lim" part of the notation.
  4. Aug 17, 2014 #3


    User Avatar
    Science Advisor

    Yes, the limit of N is the same as the limit of [itex]n^2[/itex] as n goes to infinity. And what is that limit? It's pretty obvious but you should say it.
  5. Aug 17, 2014 #4
    I think it would go to e.
    Thanks for your help!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted

Similar Discussions: Finding the limit of a sequence
  1. Limit of a sequence (Replies: 11)