Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Infinite series problem

  1. Nov 19, 2006 #1
    Hello i have the infinite series


    How do i find what it converges to if it does converge.

    Limit comparison does me no good. I am thinking integral and ratio test.

    root test does me no good either.
  2. jcsd
  3. Nov 19, 2006 #2
    Think geometric series, the ratio test also works nicely and is probably easier than trying to make this look more like a geometric series. The root test should work as well, but I think it would be a little tricky.
    Last edited: Nov 19, 2006
  4. Nov 19, 2006 #3


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    A simpler way, see if you can re-write it as a series in terms of (7/8)k
  5. Nov 22, 2006 #4
    Thanks for the replies, I applied the ratio test.

    7^K+1+1 2^3k-1 7^k (x) 7^2 2^3k (x) 2^-1
    --------- x ---------- = ----------------- x --------------
    2^3k-1+1 7^k+1 2^3k 7^k (x) 7^1


    So everything but the 7^2 which is 49 and 2^-1 / 7 which is 24.5 / 7 , which gives me 3.5, however i think this is wrong.
  6. Nov 22, 2006 #5


    User Avatar
    Staff Emeritus
    Science Advisor

    You say "thanks for the replies" but simply ignore them?

    Your calculation is completely wrong:
    7^K+1+1 2^3k-1 7^k (x) 7^2 2^3k (x) 2^-1
    --------- x ---------- = ----------------- x --------------
    2^3k-1+1 7^k+1 2^3k 7^k (x) 7^1
    is wrong. You are adding 1 to k, not to the exponent. It should be:
    [tex]\frac{7^{(k+1)+1}}{2^{3(k+1)-1}}= \frac{7^{k+2}}{2^{3k+2}}[/tex].

    In any case, it is far simpler to do as both d_leet and Office Shredder suggested: write this as a geometric sequence with common ratio 7/8. That way, it is not only obvious that the sequence converges but easy to see what it converges to!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Infinite series problem
  1. Infinite series (Replies: 1)

  2. Infinite Series (Replies: 11)

  3. Infinite Series (Replies: 2)