Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

ParthKohli

Notation of a sequence: What do we mean by \(n \ge 1\) in \(\{ 2^n\}_{n \ge 1}\)? Is it all the terms of the sequence only have \(n = 1\) or more? So basically \(n\) iterates to the positive numbers.

  • one year ago
  • one year ago

  • This Question is Closed
  1. ParthKohli
    Best Response
    You've already chosen the best response.
    Medals 2

    So, the sequence is \(\{2,4,8,16\cdots \}\).

    • one year ago
  2. ParthKohli
    Best Response
    You've already chosen the best response.
    Medals 2

    Am I correct?

    • one year ago
  3. ParthKohli
    Best Response
    You've already chosen the best response.
    Medals 2

    @agentx5 I need a genius for this.

    • one year ago
  4. agentx5
    Best Response
    You've already chosen the best response.
    Medals 1

    Powers of two, while n is greater than or equal to 1. Yep! You're good

    • one year ago
  5. agentx5
    Best Response
    You've already chosen the best response.
    Medals 1

    Infinite sequence in fact, right? (i.e.: what's the limit as n goes to infinity for 2\(^n\) ? ) ;-)

    • one year ago
  6. ParthKohli
    Best Response
    You've already chosen the best response.
    Medals 2

    Ah! Great stuff! \(\{ 1,2,3,4,5,6,7\} = \{n \} _{7 \ge n \ge 1}\)

    • one year ago
  7. ParthKohli
    Best Response
    You've already chosen the best response.
    Medals 2

    It never reaches anywhere, so it's infinity. That was an oral question :P

    • one year ago
  8. agentx5
    Best Response
    You've already chosen the best response.
    Medals 1

    This is how you typically see these though, as series (sums of the terms in a sequence) \(\sum_{n \ge 1}^{\infty} 2^n\) = \(\infty\) or "Diverges" as they say

    • one year ago
  9. ParthKohli
    Best Response
    You've already chosen the best response.
    Medals 2

    |dw:1342971644614:dw|

    • one year ago
  10. ParthKohli
    Best Response
    You've already chosen the best response.
    Medals 2

    But what if \(n\) is negative?

    • one year ago
  11. agentx5
    Best Response
    You've already chosen the best response.
    Medals 1

    n isn't negative. or zero

    • one year ago
  12. agentx5
    Best Response
    You've already chosen the best response.
    Medals 1

    It starts at 1.

    • one year ago
  13. ParthKohli
    Best Response
    You've already chosen the best response.
    Medals 2

    Oh, okay.

    • one year ago
  14. ParthKohli
    Best Response
    You've already chosen the best response.
    Medals 2

    What if we have negatives included?

    • one year ago
  15. agentx5
    Best Response
    You've already chosen the best response.
    Medals 1

    \(\{n \} _{7 \ge n \ge 1}\) <--- this however has an upper boundary

    • one year ago
  16. agentx5
    Best Response
    You've already chosen the best response.
    Medals 1

    2^7 = 128

    • one year ago
  17. agentx5
    Best Response
    You've already chosen the best response.
    Medals 1

    so... {2,4,8,16,32,64,128}

    • one year ago
  18. ParthKohli
    Best Response
    You've already chosen the best response.
    Medals 2

    The limit is 0 if we have \(\{ 2^n\}_{n \le 0}\) right?

    • one year ago
  19. ParthKohli
    Best Response
    You've already chosen the best response.
    Medals 2

    I believe that the sequence \(\{2,4,8,16,32,64,128 \}\) doesn't have a limit.

    • one year ago
  20. agentx5
    Best Response
    You've already chosen the best response.
    Medals 1

    Well for one thing you've got the wrong graph here, what happens when you raise to a negative power?

    • one year ago
  21. ParthKohli
    Best Response
    You've already chosen the best response.
    Medals 2

    Exactly, we have it getting closer to 0.

    • one year ago
  22. agentx5
    Best Response
    You've already chosen the best response.
    Medals 1

    |dw:1342971841230:dw|

    • one year ago
  23. ParthKohli
    Best Response
    You've already chosen the best response.
    Medals 2

    Starts at 1 and keeps getting closer to 0.

    • one year ago
  24. ParthKohli
    Best Response
    You've already chosen the best response.
    Medals 2

    Hmm.

    • one year ago
  25. ParthKohli
    Best Response
    You've already chosen the best response.
    Medals 2

    Oops. I posted the graph for \(x^2\).

    • one year ago
  26. ParthKohli
    Best Response
    You've already chosen the best response.
    Medals 2

    \[\lim _{x \to -\infty} 2^x = 0\] Good enough?

    • one year ago
  27. agentx5
    Best Response
    You've already chosen the best response.
    Medals 1

    Yep sure does, as you approach negative infinity \[\huge \lim_{x \rightarrow -\infty} 2^x = 2^{-\infty} = (\frac{1}{2^{\infty}}) = \frac{1}{\infty} = 0\]

    • one year ago
  28. agentx5
    Best Response
    You've already chosen the best response.
    Medals 1

    See how the Algebra keeps coming back?

    • one year ago
  29. ParthKohli
    Best Response
    You've already chosen the best response.
    Medals 2

    It does =)

    • one year ago
  30. ParthKohli
    Best Response
    You've already chosen the best response.
    Medals 2

    I believe that I'd owe you a lot when I get into MIT :)

    • one year ago
  31. agentx5
    Best Response
    You've already chosen the best response.
    Medals 1

    I'm used to tutoring students with learning disabilities :-) That's my part-time job on campus. Maybe you can help me find a job at some point in the future, ya never know ^_^

    • one year ago
  32. ParthKohli
    Best Response
    You've already chosen the best response.
    Medals 2

    Heh. You're a nice guy!

    • one year ago
  33. ParthKohli
    Best Response
    You've already chosen the best response.
    Medals 2

    And nice guys don't finish last ;)

    • one year ago
    • Attachments:

See more questions >>>

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.