Since the network is infinite, if you extend the network by one more copy of the pattern, the equivalent resistance shouldn't change. So represent the network's resistance with a single resistor with Req resistance. Now, can you add 3 resistors to the Req resistor to make it back into the...
Well, the next time you start examining the effects of your particle accelerator bunny exterminator on cute pink flying bunny rabbits and wish it could effect them more, don't come complaining to me when you drown in your own pool of rabbits.
--J
Looks like you got it.
And just in case you were interested, here's some plots of the fourier series truncated to 5, 15, 50, and 500 terms. Can't even tell it's not the function itself in the 500 one, can ya'?
Good job.
--J
You got an extra negative. \cos{n\pi} = (-1)^n, which we can verify by noting that when n = 0, n\pi = 0, so \cos{n\pi} = 1. Additionally, when n = 1, we just have cosine of pi, which is -1. So we must have (-1)n instead of (-1)n-1.
--J
In what instances? Sometimes "affect" is the correct word, and sometimes "effect" is the correct word. Naturally, most of the English speakers in the world have no idea that they are not the same word, so it can be pretty irritating if it's one of your pet peeves.
--J
You need to revisit your bn with your newly refound knowledge of the behavior of sine and cosine.
The sign of your an term is indeed incorrect.
Why do I let myself get dragged into other people's problems? *sighs* Back to finals! Work, damn me!
--J
Unfortunately, it's a 30 hour drive that must be completed in one weekend. Sometimes I wonder about the things I get myself into... But there's a bubble bath waiting for me at the end of it, so it'll all be worth it.
And while I'm driving for two days straight, you get to wander around in...
*sighs* If only I didn't have to write an essay and do a few more finals, move out of my room, then drive for 30-some-odd hours, I could look into it more. But alas, I've been screwed by finals week. :frown:
So don't bust your butt on my account, salty, because I won't be able to do...
Also, you shouldn't include the xn in your coefficients. Remember that these are the coefficients of the powers of x! They don't include the power of x themselves. You must multiply them by the appropriate power of x to get your solution. Otherwise, it looks like you're set. Good job.
--J
You know that there must be two arbitrary constants because the differential equation is of second order. You select the 0 and 1 constants because they are generally the most convenient when you have these problems that are designed to work out nicely. If your differential equation were instead...