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Math2400

  • one year ago

Match each of the power series with its interval of convergence.

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  1. Math2400
    • one year ago
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    Is this right? i only get one try so I wanted to be sure i got them ><

  2. anonymous
    • one year ago
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    Ill work them myself real quick to see

  3. Math2400
    • one year ago
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    aww thanks @Concentrationalizing i can post my work if that's easier

  4. anonymous
    • one year ago
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    I have better luck working it myself. Ive noticed that I can miss something a student does wrong if I just scan their work.

  5. Math2400
    • one year ago
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    haha sounds good :)

  6. anonymous
    • one year ago
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    1st one is fine.

  7. Math2400
    • one year ago
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    kk :)

  8. anonymous
    • one year ago
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    3 and 4 need to be flip-flopped

  9. anonymous
    • one year ago
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    Ill show the work

  10. Math2400
    • one year ago
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    kk thanks :)

  11. Math2400
    • one year ago
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    so it is C,B,D,A

  12. Math2400
    • one year ago
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    And if i could see ur work i'd appreciate that :)

  13. anonymous
    • one year ago
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    Via root test on #3 \[\lim_{n \rightarrow \infty} \sqrt[n]{\left| \frac{ (x-9)^{n} }{ 9^{n} } \right|}\] \[= \left| x-9 \right|\cdot \lim_{n \rightarrow \infty}\frac{ 1 }{ 9 } = \frac{ 1 }{ 9 }\left| x-9 \right|\] All the n's cancel and this is your limit. The conditions for root test are the same as for ratio test, we need to be less than 1. Thus we have: \[\frac{ 1 }{ 9 }\left| x-9 \right| < 1 \implies \left| x-9 \right| < 9\] which would give you the (0,18) result (since its multiple choice, I assume we dont need to actually check the endpoints)

  14. anonymous
    • one year ago
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    i will not butt in and let @Concentrationalizing finish, but i am willing to bet you can guess at least two of these doing no work now i will go away

  15. anonymous
    • one year ago
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    Via ratio test on #4 \[\lim_{n \rightarrow \infty}\left| \frac{ (x-9)^{n+1} }{ (n+1)!9^{n+1} }\cdot \frac{ 9^{n}n! }{ (x-9)^{n} } \right|\] \[= \left| x-9 \right|\lim_{n \rightarrow\infty}\left| \frac{ 9^{n}n! }{ 9(n+1)9^{n}n! } \right|\] \[= \left| x-9 \right|\lim_{n \rightarrow \infty}\left| \frac{ 1 }{ 9(n+1) } \right| = 0\] So all values of x work since we got a result of 0

  16. anonymous
    • one year ago
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    I could guess them, but I'm not comfortable enough doing that yet, I'd rather just do the work and make sure I'm correct, lol @satellite73 Anyway, normally these aren't multiple choice x_x

  17. Math2400
    • one year ago
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    haha thanks :)

  18. anonymous
    • one year ago
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    No problem :)

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