Recent content by Kyousik

  1. K

    How Does the Biot-Savart Law Apply to a Wire Shaped in Two Half Circles?

    B = (Mu * I) / (2 * Pi * a); where R = a; I = Ienclosed.
  2. K

    How Does the Biot-Savart Law Apply to a Wire Shaped in Two Half Circles?

    Homework Statement "A wire is formed into the shape of two half circles connected by equal-length straight sections. A current I flows in the circuit clockwise as shown. Determine (a) The magnitude and the direction of the magnetic field at the center, C, and (b) the magnetic dipole moment of...
  3. K

    Solving the Harmonic Series and Ratio Problem

    Homework Statement (infinity)sigma(n=4) [ (2 / n) - (2 / (n -1)) ] Homework Equations Harmonic series and ratio? The Attempt at a Solution It's supposed to converge to -2/3, but, I don't know how. The first compare to a harmonic series and we see that goes to 0. The second...
  4. K

    First test of divergence lim n-> n / 8^n

    Homework Statement n / 8^nHomework Equations The Attempt at a Solution It converges to 8 / 49? Not sure how. First test of divergence lim n-> n / 8^n. infinity / infinity = 1. BUT bottom grows fast. Using L`Hospital lim n -> 1 / 3*8^n*ln(2) ---> goes to 0 Tried to use the ratio test [ 1 /...
  5. K

    Radius of Convergence: f(x) = x^4 / (2 - x^4)

    Homework Statement f(x) = x^4 / (2 - x^4). Specify radius of convergence. Homework Equations Power Series f`(x) = c2 + 2c2(x-a) + 3c3(x-a)^2 + ... = (infinity)sigma(n=1) [n * cn * (x-a)^(n-1)] The Attempt at a Solution I'm not sure what to do. Usually, most problems are like x^3 /...
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    Geometric Series: 2/3^k and -2/10^k

    So to prove that, I would use the ratio test to show absolute convergence? Absolute convergence was very confusing reading from the textbook. I forgot there were other ways to show absolute convergence. Like using harmonic, or comparison or something.
  7. K

    Geometric Series: 2/3^k and -2/10^k

    Oh oops! I see, the |r| value is the ratio. Not the number you get after. The number you get after is what the series converges to? So 3 + 5/6 = 18 / 6 + 5 /6 --> 23 / 6 Would that be correct?
  8. K

    Geometric Series: 2/3^k and -2/10^k

    Homework Statement (infinity)sigma(k = 0) [2(2/6)^k + (-2/10)^k) Homework Equations Geometric Series The Attempt at a Solution I split these up into two geometric series (infinity)sigma(k = 0) [2(1/3)^k] 2 / (1 - 1/3) r = 3 This diverges. (infinity)sigma(k = 0) (-1/5)^k...
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