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Math Help - finding the interval of convergence..

  1. #1
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    finding the interval of convergence..

    in the first problem i was asked to find the interval of convergence and then i was supposed to check the endpoints, im not sure if i did this problem right and was wondering if someone could check my work and tell me where i went wrong. in the next problem i was supposed to find a geometric series, which seemed easy enough, but please check both problems. thanks in advance..IMG.pdf
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  2. #2
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    Quote Originally Posted by slapmaxwell1 View Post
    in the first problem i was asked to find the interval of convergence and then i was supposed to check the endpoints, im not sure if i did this problem right and was wondering if someone could check my work and tell me where i went wrong. in the next problem i was supposed to find a geometric series, which seemed easy enough, but please check both problems. thanks in advance..IMG.pdf


    The first series is one around x=2 and its convergence radius is \frac{1}{3} , since you got 3|x-2|<1\iff |x-2|<\frac{1}{3} .

    Besides this, the series converges at x=\frac{5}{3} (you get the alternating harmonic series), but diverges at \frac{7}{3} (you get the harmonic series), so the interval of conv. is \left[\left. \frac{5}{3}, \frac{7}{3}\right.\right).

    The second question is written, apparenty, in sumerian mixed with ancient sanscrit, but if I have to guess you're asked to find a power series for that function h(x), and yes: what you did is correct.

    Tonio
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  3. #3
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    Fortunately, I speak both Sumerian and Sanscrit (as well as practice reading really bad handwriting- mine)! The first line is "Find a geometric power series centered at 0".

    Yes, your solution is correct.
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  4. #4
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    i was really tired when i did those problems, besides prep for the calc final i had to write an economic analysis?? thanks again im going to definitely start doing more problems when im not so tired. LOL
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    Quote Originally Posted by HallsofIvy View Post
    Fortunately, I speak both Sumerian and Sanscrit (as well as practice reading really bad handwriting- mine)! The first line is "Find a geometric power series centered at 0".

    Yes, your solution is correct.


    Fine , but if the series was to be centered at zero then it perhaps is nicer to write it as

    \sum^\infty_{n=1}\frac{3}{2}\left(-\frac{x}{2}\right)^n=\sum^\infty_{n=0}(-1)^n\frac{3}{2^{n+1}}\,x^n

    Tonio
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