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2/15/05
2/14/05

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Venice

Venice

SUICIDEGIRL

Oregon, USA

FEB 14, 2005 02:47 PM

Al said:
Dude, take number theory without a calculator. That makes you good at addition and subtraction REAL fast.



I would, in fact I intended to, but the damn class is only offered every other year, including this year, and I am not there currently to benefit from it. I hate shit like that.

[Edited on Feb 14, 2005 by Venice]

[Edited on Feb 14, 2005 by Venice]

delusion

delusion

Santa Barbara, CA
March 2004

FEB 14, 2005 02:53 PM

I just took Calculus over the summer but, I never would have passed if it weren't for Maurauder's patient tutorial. She's pretty much the hottest math whiz ever.

MisterSatan

MisterSatan

Vancouver, WA
August 2002

FEB 14, 2005 05:18 PM

revonrat said:

threejane said:

Prove that sum(i^3, 1..n) = (n^2*(n+1)^2)/4


By induction:
For n=1: obvious.

Assume that sum(i^3, 1...k) = (k^2*(k+1)^2)/4
Then sum(i^3, 1...(k+1)) = (k^2*(k+1)^2)/4 + (k+1)^3
= (k^4 + 2k^3 + k^2)/4 + (4k^3 + 12k^2 + 12k + 4)/4
= (k^4 + 6k^3 + 13k^2 + 12k + 4)/4

Now look at (k+1)^2*(k+2)^2/4 = (k^2 + 2k + 1)(k^2 + 4k + 4)/4
= (k^4 + 6k^3 + 13k^2 + 12k + 4)/4

So sum(i^3, 1...(k+1)) is equal to (k+1)^2*(k+2)^2/4, which completes the proof by induction.


Awe ... That one was for MisterSatan. At least if you were going to spoil it, you could have had the decency to be female
frown


That's okay; I ignored it because I asked for a problem to solve, not prove.

threejane

threejane

San Francisco, CA
November 2004

FEB 14, 2005 05:44 PM

MisterSatan said:
That's okay; I ignored it because I asked for a problem to solve, not prove.



Given an NxN uniform square grid in the plane, select two points at random (uniform probability) on the grid. Draw the line segment connecting these two points. Now select a third point on the grid at random (again, uniform probabilities). What is the probability that the third point falls on the line segment?

MisterSatan

MisterSatan

Vancouver, WA
August 2002

FEB 14, 2005 06:00 PM

threejane said:

MisterSatan said:
That's okay; I ignored it because I asked for a problem to solve, not prove.


Given an NxN uniform square grid in the plane, select two points at random (uniform probability) on the grid. Draw the line segment connecting these two points. Now select a third point on the grid at random (again, uniform probabilities). What is the probability that the third point falls on the line segment?


I'll get back to you when I'm not at work.

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