L.sufiya Khanam posted an Question
October 08, 2020 • 13:02 pm 30 points
  • IIT JAM
  • Mathematics (MA)

Clarification

plz give some examples. for this. theorem. ??

1 Answer(s) Answer Now
  • 0 Likes
  • 2 Comments
  • 0 Shares
  • comment-profile-img>
    Piyush pachauri

    you should try to construct example on your own that will help you. Take an = 2-(3/n) converges to 2 here m=1

    eduncle-logo-app

    sir here Xn will be -1 ,1/2 ,1, 5/4........

    eduncle-logo-app

    here Xn is -1 which is not greater than 0

    eduncle-logo-app

    but in theorem Xn is greater than 0

    eduncle-logo-app

    It says xn > 0 for all n>m

    eduncle-logo-app

    after some natural no m , Xn should be greater than zero.

    eduncle-logo-app

    ok sir

  • Srinath Best Answer

    This theorem states the simple fact that, when a sequence converges to a positive real number, all but a finite number of terms in the sequence has to be positive. That is, while approaching a positive real number at the limit, there are infinite terms of the sequence at the tail end, that are all positive. For example, consider the sequence, {n/(n+1)}. This sequence converges to 1, and there are infinite number of positive terms, (an) for any n. If this example isn't satisfactory, try (-1)^n/n

    eduncle-logo-app

    sir for the second example limit is zero right?

    eduncle-logo-app

    Yes, I forgot to type, 1 + ((-1)^n/n)

    eduncle-logo-app

    but still it's not satisfactory as limit is 0, that is it's not greater than zero right?

    eduncle-logo-app

    What you are saying is right. I wanted to type 1+ ((-1)^n/n), but I typed it without the 1, so it's limit becomes 0, which cannot be used in this scenario.

    eduncle-logo-app

    okay sir, im telling that without 1 also it is not satisfactory right?

    eduncle-logo-app

    Yes, it is not. Limit has to be greater than 0.

    eduncle-logo-app

    ok sir 👍

whatsapp-btn

Do You Want Better RANK in Your Exam?

Start Your Preparations with Eduncle’s FREE Study Material

  • Updated Syllabus, Paper Pattern & Full Exam Details
  • Sample Theory of Most Important Topic
  • Model Test Paper with Detailed Solutions
  • Last 5 Years Question Papers & Answers