Earlier quoted context omitted.
It's necessary that one number is absent. The period is 2997 as he mentions. Can't pack 1000 3 digit numbers into that ;)
Chuck Norris could :P
No sense of humor. Seriously.
Fun with math: Dividing one by 998001 yields a surprising result
71–80 of 99 posts
Re: Fun with math: Dividing one by 998001 yields a surprising result
#72That's nothing!
6922251 * 8 on a calculator spells my ex's nickname....
Re: Fun with math: Dividing one by 998001 yields a surprising result
#73Earlier quoted context omitted.
Chuck Norris could :P
No sense of humor. Seriously.
It isn't about having, or not having, a sense of humor. It's just that Hacker News culture prides itself on maintaining a certain decorum to the discussion here... and it doesn't include internet memes, Chuck Norris jokes, or a lot of the other frivolous stuff that's accepted on Reddit, Digg, Slashdot, etc.
It's not that people here are stuffy, or humorless, or anything; we just want HN to be different, and not decay into a festering cesspool of malfeasance like Slashdot or whatever. There are plenty of places one can go to get that kind of stuff on the 'net. Here at HN, it will usually be downvoted mercilessly.
Re: Fun with math: Dividing one by 998001 yields a surprising result
#74Re: Fun with math: Dividing one by 998001 yields a surprising result
#75Earlier quoted context omitted.
Here is a more detailed explanation 1--------- If x = 0.001 then the sum x^2 + 2 x^3 + 3 x^4…. in its decimal places will have all the three digit numbers except the the second last starting with 000,001 and then till 997,999. As pointed out by someone below,the reason 998 is missing is because after 997998999 the next coefficient is 1000.This overflow 1 will carry over and mess up all the nines to the right until it…
A quicker proof is to just differentiate. For |r| 1 + r + r^2 + ... = 1/(1-r) Differentiate both sides of the equation: 1 + 2r + 3r^2 + ... = 1/(1-r)^2 Here's a bijective combinatorial proof, which I like best of all. It uses the concept of generating functions. As a caveat, it only shows the equality for formal power series, not analytic power series. The series 1 + r + r^2 + ... = 1/(1-r) is the type of tuples with…
Thanks. That's really cool.
Re: Fun with math: Dividing one by 998001 yields a surprising result
#76Earlier quoted context omitted.
For x < 1, 1 + 2x + 3x^2 + 4x^3 + ... converges to 1/(1-x)^2. When x = 0.001, you get 1/.999^2 = 1000000/998001 = 1.002003004005...
Here is a more detailed explanation 1--------- If x = 0.001 then the sum x^2 + 2 x^3 + 3 x^4…. in its decimal places will have all the three digit numbers except the the second last starting with 000,001 and then till 997,999. As pointed out by someone below,the reason 998 is missing is because after 997998999 the next coefficient is 1000.This overflow 1 will carry over and mess up all the nines to the right until it…
Here's a similar derivation (assuming |x|
x + 2x^2 + 3x^3 + 4x^2..
=
x + x^2 + x^3 + x^4 + ...
+ x^2 + x^3 + x^4 + ...
+ x^3 + x^4 + ...
+ x^4 + ...
= sum i from 0 to infinity (sum j=i to infinity (x^j))
= sum i from 0 to infinity ((x^i)/(1-x))
= 1/(1-x)^2Re: Fun with math: Dividing one by 998001 yields a surprising result
#77Some fun that can fit on a poket calculator:
12345679 * 9 = 111111111
12345679 * 18 = 222222222
12345679 * 27 = 333333333
12345679 * 36 = 444444444
12345679 * 45 = 555555555
12345679 * 54 = 666666666
12345679 * 63 = 777777777
12345679 * 72 = 888888888
12345679 * 81 = 999999999
12345679 * 999999999 = 12345678987654321
Re: Fun with math: Dividing one by 998001 yields a surprising result
#78You can find the Catalan numbers buy computing 500,000,000,000 - Sqrt(500,000,000,000*500,000,000,000 - 1)....
http://people.csail.mit.edu/devadas/numerics_demo/chord.html
For an explanation better than I can provide of what they are and how it works, see 6.006 lecture 11 notes!
http://courses.csail.mit.edu/6.006/fall11/lectures/lecture11...
Re: Fun with math: Dividing one by 998001 yields a surprising result
#79Thanks for posting. I'm trying to keep a collection of these type of things so that when she's ready, it'll be another tool to get/keep my daughter excited about math.
Care to share? Would be handy to have for my daughter... :)
I'll start a post when I have enough worth sharing. She's 4 now and we're still working with basic math. I've found a few books that incorporate math that she's enjoyed; right now we're halfway through The Phantom Tollbooth. Milo just left Dictionopolis so we're headed to Digitopolis shortly...
Re: Fun with math: Dividing one by 998001 yields a surprising result
#80A simple way to figure out how this works is to figure out another way to write it out. For the simpler case (1/9801) = 0.00010203...
0.00
+ 0.0001
+ 0.000002
+ 0.00000003
...
--------------
sum k=0 to infinity: k/(10^k)