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!

Convergence of a series

  1. Jul 15, 2016 #1
    • Member warned about posting with no effort
    1. The problem statement, all variables and given/known data
    determine whether the series below converges.
    ##\sum_{n=1}^\infty 2^n.n+1,√(n^4+4^n.n^3)##



    2. Relevant equations


    3. The attempt at a solution
     
    Last edited: Jul 15, 2016
  2. jcsd
  3. Jul 15, 2016 #2

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Useful things, brackets !

    $${\sum_{n=1}^\infty {(2^n.n+1)}\over \sqrt {n^4+4^n.n^3}} \quad \rm ?$$

    And 'whether the series ....' what exactly ?

    How about your own attempt at solution ? What instruments do you intend to usse ?
     
  4. Jul 15, 2016 #3
    sorry unable to post in latex form, i will attempt and share.
     
  5. Jul 15, 2016 #4
    ##2^n+1/√n^3(n+4^n)##
     
  6. Jul 15, 2016 #5

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Hello Chwala,

    Let me get this right. You mean $$
    2^n+ {1\over \sqrt {n^3(n+4^n)} }\quad \rm ? $$ No ? I thought so.
     
  7. Jul 15, 2016 #6
    Sorry i meant ##(2^n. n+1)/√{n^3(n+4^n)}##
    = ##(2^n. n+1)^2/{n^3(n+4^n)}##
     
  8. Jul 15, 2016 #7

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    The equals sign can't be right. Generally ##y \ne y^2 ## Which one of the two ?
    And what happened to the ##\Sigma ## ?
    And what is it we want to know about whatever the correct expression turns out to be ?
     
  9. Jul 15, 2016 #8
    agreed we just deal with y me thinks we have to try express it in geometric from and check for |r| since n=1, we have to use the n-1 form..
     
  10. Jul 15, 2016 #9

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    We still don't know where we are (what happened to the square root ?")

    And then you might also reveal where we want to go. You still haven't told us.

    My lunch break is almost over and all we did was find out what you want. Perhaps you want to check your postings before shooting them off. Try to be as dumb and precise as the worst of your readers. (me ? :smile:)
     
  11. Jul 15, 2016 #10
    hahahhahaha i will re post again only challenge is the latex.........let us consider ##(2^n. n+1)/√{n^3(n+4^n)}## as my attempt and we forget about the other step.
     
  12. Jul 15, 2016 #11

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Ok square root is back. Could you please please please stop writing a/bc -- which is equal to a/b times c -- when you really mean a/(bc). It is unforgivable in these situations. Use brackets. They are cheap (in fact, they come for free). Please confirm reception of this advice :smile: .

    1. The problem statement, all variables and given/known data
    determine whether the series below converges $$ \sum_{n=1}^{\infty} { n \;2^n +1 \over \sqrt {n^3\;(n+4^n)} } $$​

    Are we there yet ?
     
  13. Jul 15, 2016 #12

    Ray Vickson

    User Avatar
    Science Advisor
    Homework Helper

    You need not use LaTeX, and you probably should not until you can use it correctly! It can all be done reasonable clearly in plain text if you use parentheses, like this: (2^n * n+1)/sqrt[n^3 *(n + 4^n)].

    That said, I urge you to take the time to learn how to use LaTeX properly; you can right-click on displayed expressions others have written, and ask for the expression to be displayed as tex commands. Remember also: you need to tell the PF server that "latex starts here" and "latex ends here". For an in-line expression just use # # (with no space between the # and the #) at both the start and end of your expression, to get ##\text{some expression}\cdots##. For a "displayed" version, use "[ tex ]" (but with no spaces) at the start and "[ /tex ]" (no spaces) at the end, to get
    [tex] \text{some expression} \cdots [/tex]
     
  14. Jul 15, 2016 #13

    Mark44

    Staff: Mentor

    My preference for standalone LaTeX, as it entails less typing is to use $$ at the start and $$ at the end. For inline expressions, I use ## at both ends, like you said.
     
  15. Jul 16, 2016 #14

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    Soo, now we finally know the problem! So what did you already try to solve it. There are various tests that you can use, so did you try them?
     
  16. Jul 29, 2016 #15
    I looked into this one can use ratio test or a direct comparison test with a similar series................
     
  17. Jul 29, 2016 #16

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    How do you type dollar dollar :smile: $$ without $$ ending up in ## \LaTeX## ?
     
  18. Jul 29, 2016 #17

    BvU

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    And what is the result ?
     
  19. Jul 29, 2016 #18

    Mark44

    Staff: Mentor

    By changing the color of one of the $ symbols at each end.
    $$\frac{x - 1}{x + 3}$$
    In the expression above, the 2nd and 4th $ symbols have color attributes.
     
  20. Jul 29, 2016 #19

    micromass

    User Avatar
    Staff Emeritus
    Science Advisor
    Education Advisor
    2016 Award

    So what did you get with the ratio test? With what series did you compare?
     
  21. Jul 29, 2016 #20
    Bvu i will post the results soon...sorry i am on holiday am enjoying the beach of mombasa, kenya
     
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: Convergence of a series
  1. Series convergence (Replies: 26)

  2. Convergence of a series (Replies: 24)

  3. Series Convergence (Replies: 15)

  4. Series convergence (Replies: 8)

  5. Convergence of series (Replies: 13)

Loading...