Results are out! Find what you need...fast. Get quick advice or join the chat
Hey! Sign in to get help with your study questionsNew here? Join for free to post

Sum to infinity of an arithmetic progression

Announcements Posted on
Applying to Uni? Let Universities come to you. Click here to get your perfect place 20-10-2014
    • Thread Starter
    • 0 followers
    Offline

    ReputationRep:
    Ok, I'm just slightly confused.
    I have to find the sum to infinity of a series, which turns out to be arithmetic in its nature. Is it correct to find the sum from n=1 to n=n, because you clearly cannot define n=infinity.
    • 1 follower
    Offline

    ReputationRep:
    What's the series?
    • Thread Starter
    • 0 followers
    Offline

    ReputationRep:
    It's a longer series. The exact series doesn't really matter.

    How about I just write:

    Sigma[n=0, ∞]En = lim[T-->∞]Sigma[n=0, T]En

    And then solve for the limit?
    • 16 followers
    Offline

    ReputationRep:
    Surely arithmetic series diverge?
    • 0 followers
    Offline

    ReputationRep:
    (Original post by Siddhartha)
    Ok, I'm just slightly confused.
    I have to find the sum to infinity of a series, which turns out to be arithmetic in its nature. Is it correct to find the sum from n=1 to n=n, because you clearly cannot define n=infinity.
    You cant define n=infinity, but you can consider the limit as n tends to infinity.

    Also, as aleady said, an arithmetic progression diverges since its comparable to the sum of n, which is divergent. The "sum to infinity" is only really heard of in geometric series' in my experience.
    • 16 followers
    Online

    ReputationRep:
    (Original post by mr_jr)
    `in my experience.
    That's probably because you don't have much experience of convergent series other than geometric ones.

    But you can use "sum to infinity" for any series that converges; for example \sum_1^\infty \frac{1}{n(n+1)} = 1

Reply

Submit reply

Register

Thanks for posting! You just need to create an account in order to submit the post
  1. this can't be left blank
    that username has been taken, please choose another Forgotten your password?
  2. this can't be left blank
    this email is already registered. Forgotten your password?
  3. this can't be left blank

    6 characters or longer with both numbers and letters is safer

  4. this can't be left empty
    your full birthday is required
  1. By joining you agree to our Ts and Cs, privacy policy and site rules

  2. Slide to join now Processing…

Updated: October 27, 2007
New on TSR

Personal statement help

Use our clever tool to create a PS you're proud of.

Article updates
Reputation gems:
You get these gems as you gain rep from other members for making good contributions and giving helpful advice.