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...
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...
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 /...
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 /...
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.
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?
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...