Source

acetv

u/acetv

r/math•

A primitive preliminary simulation of a taxation system suggested in r/math a week and a half ago: progressive taxes based on net worth, not income.

On May 2nd, pathjumper submitted a post which proposed a progressive tax system dependent on net worth, not income. He suggested a few other things too but this was the only one I could decipher well enough. Unfortunately pathjumper acted an ass in both of the posts he made (the original was in r/reddit.com) so nothing ever came of it. Well today I was bored so I decided to see if I could figure out some of the base implications of a system such as this.

I have no background in economics (I took one micro class in college...) so I'm sure there are some obvious improvements/corrections th

35
r/math•

A simple inequality, and how it lead me to a problem which took fifty years to solve.

I had just started reading a book on inequalities (link at the end), and on page 17 I encountered the following problem:

Show that, for all positive integers n,

    [; \frac{1}{\sqrt{4n+1}} < \frac{1}{2} \cdot \frac{3}{4} \cdot \frac{5}{6} \cdot \,\cdots\, \cdot \frac{2n-1}{2n} \leq \frac{1}{\sqrt{3n+1}}. ;]

Can you improve this approximation?

If you'd like to do this problem yourself, you should ignore my post in r/cheatatmathhomework where I give a solution. There are a couple different ways to do it that I see, so after you've found one you should try finding another!

Now, what interested me was the challenge to improve the approximation. After staring at the bounds

15415
r/cheatatmathhomework•

Proving an inequality involving a product

Here it is:

(pi*n + 1)^-1/2 < product (2k - 1)/(2k) from k=1 to k=n.

Experimentally this seems true. The preceding exercise is to show

(4n + 1)^-1/2 < product (2k - 1)/(2k) from k=1 to k=n,

which is easy to verify once you realize that

(4(k-1) + 1)^1/2 (4k + 1)^-1/2 < (2k - 1)/(2k)

whenever k > 0. However I haven't had any luck adapting this method to the inequality in question, and in fact if you try optimizing

(c(k-1) + 1)^1/2 (ck + 1)^-1/2 <= (2k - 1)/(2k)

for the unknown c, the best you can do is 4, no less. So I really do think this approach is a dead end.

Just one last thing. I don't know if it helps, but we can trade the product notation for factorials. Th

35
r/halifax•

I'm moving to Halifax for school in the Fall and was wondering if you guys could help me out with some questions I have.

My SO and I will both be attending Dal this Fall and so we've been on the prowl for a place (for about a month now). These are the questions that have come up so far:

1. With regards to electricity bills...

I've had several places where this is not included in the monthly rent and so I have to brace myself, cover my eyes, and just ask them for an estimate. The damage is usually not bad at all-- a typical response for a one bedroom apartment is that it runs about $40- $60 every other month.

Now, I then asked a two bedroom place what I could expect for electricity. The fella said it would be about $375/mo in the "dead of winter", but that averaged over the year it would be about $

1031
r/cheatatmathhomework•

Which grows faster: (n!)! or ((n-1)!)!(n-1)!^n!

This is exercise 2(b) in chapter 9 of Concrete Mathematcs.

Which grows faster: (n!)! or ((n-1)!)!(n-1)!^n!

My first approach was to replace n-1 with n in the second formula to get (n!)!n!^(n+1)! which would clearly grow faster than than the first formula, but I realized that this argument was using some iffy logic.

The back of the book merely gives the solution with a small hint: Take logarithms to show that (n!)! wins.

Well ok, let's take some logarithms. We get

log[(n!)!]

    = log[n!(n!-1)(n!-2)...(n-1)!((n-1)!-1)((n-1)!-2)...3\*2\*1]

    = log[n!(n!-1)(n!-2)...((n-1)!+2)((n-1)!+1)((n-1)!)!]

    = log n! + log(n
63
r/math•

Using finite calculus to find the partial sums of an infinite series

Ever since I read the awesome paper Finite Calculus: A Tutorial for Solving Nasty Sums [PDF] by David Gleich I've been itching for an opportunity to show off its usefulness.

Yesterday, dsh1202 posted a [question in r/cheatatmathhomework](http://www.reddit.com/r/learnmath/comments/gy7ub/sum_of_a_series/) which asked how to evaluate the series from 2 to infinity of 4/(n(n+2)).

Here's a link to my reply, where I outline the general method of using finite calculus to solve the problem.

http://www.reddit.com/r/learnmath/comments/gy7ub/sum_of_a_series/c1ra9qn

If you're familiar with calcu

5429