I'm a domestic student planning on applying to PhD programs in physics this fall but I am concerned with my lack of research experience. I realize this is an odd position to be in but I'm deeply interested in physics and think I'm an otherwise good candidate for graduate study. I'm interested in...
Homework Statement
(x^2)y' = y
Homework Equations
The Attempt at a Solution
Plugging in series everywhere I get the equation \sum na_{n}x^{n+1} = \sum a_{n}x^{n}. I try to set the coefficients for the corresponding powers equal, but when I do I don't get the correct answer. I also...
Homework Statement
You are sitting by a window when someone on the roof drops a ball. The ball spends .30 seconds in front of the window (which is 1.50 meters tall.) The ball subsequently hits the sidewalk and bounces back up at the same speed. On its way up it passes by the window again...
I was doing my math homework when I started thinking about the sums of two infinite series.
I determined that the sum of the first series \sum_{n=1}^{\infty} cos(\frac{\pi}{2n}) diverges. I could not figure out whether or not the series \sum_{n=1}^{\infty} sin(\frac{\pi}{2n}) converges or...
Homework Statement
Find the vertical asymptotes of the graph of the function. (Use n as an arbitrary integer)
\frac{tanx}{x}
Homework Equations
N/A
The Attempt at a Solution
I believe the answer is x=\frac{\pi(2n+1)}{2}. I would just like somebody to confirm or deny this. Thanks...
Homework Statement
Prove that
11^n - 4^n
is a multiple of 7
Homework Equations
N/A
The Attempt at a Solution
I substituted k+1 in for n and simplified to get
11(11^k)-4(4^k)
but after this point I get stuck. Any help would be appreciated.
Homework Statement
Determine whether the sequence with the given nth term is monotonic. Find the boundedness of the sequence.
a_n = ne^{-n/2}
Homework Equations
I don't know
The Attempt at a Solution
I have absolutely no idea what a monotonic sequence is or how to find the...