Homework Statement
Let b be a positive integer and consider any set S of b+1 positive integers.
Show that there exists two different numbers x, y ∈ S so that x mod b = y mod b
Homework Equations
The Attempt at a Solution
Pretty stumped. I tried for a while to use different values...
Hello all,
so I'm sick of connecting wirelessly from my router (in the bottom, rear, west corner of my house) to the room where I do all of my work (the top, front, east corner). I decided I'm going to run a cable along the outside of the house and into the work room.
The cable will not be...
Homework Statement
I need to fin the sum of the following two infinite series:
1. Ʃ[n=0 to ∞] ((2^n + 3^n)/6^n)
and 2. Ʃ[n=2 to ∞] (2^n + (3^n / n^2)) (1/3^n)
Homework Equations
use the sum Ʃ[n=2 to ∞] (1/n^2) = ∏^2 / 6 as necessary
The Attempt at a Solution
I tried to manipulate them...
Homework Statement
I need to use the Comparison Test or the Limit Comparison Test to determine whether or not this series converges:
∑ sin(1/n^2) from 1 to ∞
Homework Equations
Limit Comparison Test: Let {An} and {Bn} be positive sequences. Assume the following limit exists:
L =...
Ok, so I'm a little confused about why <p> = 0 for Hydrogen in the ground state. If someone explain the reasoning behind this, I'd greatly appreciate it.
Also, and more importantly, does that mean that <p> = 0 for Hydrogen in other states as well? If not, how would you go about finding <p>...
Homework Statement
I'm trying to calculate delta r * delta p for the Hydrogen atom in the 2s stateHomework Equations
ψ(r) = (1/ 2√π) (1 / 2a)^(3/2) (2 - (r/a)) e^(-r/2a)
where a is the bohr radiusThe Attempt at a Solution
I figured out that <r> = 6a, but I'm at a loss as to how to figure out...