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 general term of the series

  1. Sep 21, 2014 #1
    1. The problem statement, all variables and given/known data

    Find the general term and test the nature(convergent/divergent) of:
    1/3 + 2/15 + 2/35 + .....

    3. The attempt at a solution
    If I simplify I get ,
    1/3 + (1)(2)/(3)(5) + (1)(2)(3)/(3)(5)(7) +.............

    I found that,
    TERM(N) = TERM(N-1)((N)/(2N+1)

    After this I am struck.
     
  2. jcsd
  3. Sep 21, 2014 #2
    The new format of this website is difficult for me.
     
  4. Sep 21, 2014 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    You see, I suspect, that the numerator of the nth term is n! The denominator is something like a factorial except that it involves only odd integers- okay, make it a factorial by inserting the even integers:
    [tex]\frac{1}{3*5*7}= \frac{2*4*6}{2*3*4*5*6*7}= \frac{2*4*6}{7!}[/tex]

    Now, factor a 2 out of each term in the numerator: 2*4*6= 2(1)*2(2)*2*3= 2^3(3!).

    So [tex]\frac{1}{3*5*7}= \frac{2*4*6}{2*3*4*5*6*7}= \frac{2^3(3!)}{7!}[/tex]

    Your term [tex]\frac{1*2*3}{3*5*7}= \frac{2^3(3!)^2}{7!}[/tex].

    Can you write the nth term now?

    Do you see n
     
  5. Sep 21, 2014 #4
    yeah... i can write the nth term and i found that the series is convergent.

    But this series:
    1/4 + (1)(5)/(4)(8) + (1)(5)(9)/(4)(8)(12) + ...

    The general term for the denominator is 4^n (n!)

    but the numerator terms are tricky : 1*5*9

    ==> 1*2*3*4*5*6*7*8*9/2*3*4*6*7*8

    ==>9!/2*3*4*6*7*8

    how do i simplify this part : 2*3*4*6*7*8 ?
     
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 general term of the series
  1. Find no. of terms (Replies: 9)

Loading...