The Math Help Topic

[stan423321]

I've got a question!
What's faster way of counting that?
(1*n) + (2*(n-1)) + ... + ((n-1)*2) + (n*1)

[Hunchman801]

n(n+1)²/2 - n(n+1)(2n+1)/6 = n(n+1)(n+2)/6.

[stan423321]

Are you sure? Thanks.

[Hunchman801]

Well yeah, you just have to write it as the sum of i(n+1-i) and to develop the whole thing.

[Tobbe]

I had my math finals today. It went well but there's one thing I couldn't figure out, and it's been bugging me all day. Could someone please solve this differential equation:


y''+2xy'+2y=2

y(0)=0 and y'(0)=0

This is probably ridicolously easy by international standards, but don't blaim me; blaim the crappy level of science and math education in the Norwegian high school.

[Hunchman801]

There is no general expression for the solutions of a second-order linear differential equation with non-constant coefficients. There's probably a simple way but I studied this three or four years ago so I don't really remember anything

WolframAlpha found it anyway: 1-e-x².

Edit: after a few minutes I found it: y''+2xy'+2y = (y'+2xy)'. The first-order linear equation can be solved easily, and then I'm pretty sure you can do the rest with the constants and everything.
Good to know I can still do math after so many years

[Matyuv]

guys can somebody help me with this? it's probably not too hard but I keep getting bullshit in the end

it's the exam period and I'm pretty desperate

[DesLife]

I assume you've tried to integrate it by parts ?

[Hunchman801]

Well I don't really have time to give it a try tonight but I quickly found out that ∫xdx/√((x-a)(b-x)) = ((a+b)/2)×∫dx/√((x-a)(b-x)) (you just have to integrate (a+b-2x)dx/√((x-a)(b-x))). I'm going to bed now but I'll see what can be done tomorrow when I get back from work.

[Matyuv]

Yeah that's what I was doing too, and after some work with the demoninator and integrating it I got a couple of -infinities which can't be right... I'll have to recheck it

edit
yes apparently I'd fucked up before, now I get arcsin((2x-(a+b))/(a-b)) which seems better ;O
wolframalpha doesn't agree though

[DesLife]

I got (a+b)*Pi/2 : (a+b)/2 * Arcsin (2u/(b-a)) from (a-b)/2 to (b-a)/2. (With u = x - (a+b)/2)
I'm sure this is good. If you derivate this Arcsin, you get (a+b-2x)dx/√((x-a)(b-x))), which is, as Hunch said, equal to your integral.

[Hunchman801]

I have to say guys, we are definitely the most awesome Rayman forum ever

[DesLife]

I have to say guys, we are definitely the most awesome forum ever

I need a strike tag !
Do you have some softwares you can use to write maths (with all the symbols needed, sums, integrals, limits, fractions...) ?
Edit : nevermind, even that piece of shit known as Word provides this.

[Matyuv]

OK thank you guys =)

P.S.: strike tag = do want

[Hunchman801]

P.S.: strike tag = do want

No way.

[Matyuv]

P.S.: strike tag = do want

No way.

Cheers.

[DesLife]

P.S.: strike tag = do want

No way.

Cheers.

Yaay ! Thanks Hunch

[PluMGMK]

Thank you!

[Matyuv]

For those of you who are into programming and maths here's a link - http://projecteuler.net/index.php?section=about

Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. Although mathematics will help you arrive at elegant and efficient methods, the use of a computer and programming skills will be required to solve most problems.

It's got some nice problems to solve... I've solved 4 so far lel.

[DesLife]

Thanks Matyuv, that seems funny ! Solved the first one, took me some time cause I added the multiples of both 3 and 5 twice, forgot to substract them.
I hope the next ones are harder