ben1996123
Banned
S=a+ar+ar²+...+ar^(n-1) (n terms)
Sr=ar+ar²+ar³+...+ar^n
S-Sr=S(1-r)=a-ar^n=a(1-r^n)
S=a(1-r^n)/(1-r)
for sum to iniffity, r^n -> 0 as n->iniffity if -1<r<1 so S=a/(1-r)
Mathematics Thread
- Thread starter IanTheCuber
- Start date
S=a+ar+ar²+...+ar^(n-1) (n terms)
Sr=ar+ar²+ar³+...+ar^n
S-Sr=S(1-r)=a-ar^n=a(1-r^n)
S=a(1-r^n)/(1-r)
for sum to iniffity, r^n -> 0 as n->iniffity if -1<r<1 so S=a/(1-r)
Kit Clement
Premium Member
- Joined
- Aug 25, 2008
- Messages
- 1,626
- Location
- Champaign, IL, USA
- WCA ID
- 2008CLEM01
- YouTube
- Visit Channel
Here's a fun integral I came across on my statistical inference homework today. You can easily find the numerical answer via wolfram, but their indefinite solution uses error functions, so coming up with a solution by hand is kind of tricky.
http://bit.ly/1isXHMg
And here's the final numerical answer, if you want to verify your integral is correct.
http://bit.ly/17w2JGn
http://bit.ly/1isXHMg
And here's the final numerical answer, if you want to verify your integral is correct.
http://bit.ly/17w2JGn
ben1996123
Banned
ifink substitute u=x/β so its βint e^-u² du from 0 to iniffity
converting to polar turns ue^-u² or something like that wich is indefinitely integrable and its sqrt(pi)/2 or something so i fink d anser is β/2 sqrt(pi) ??
edit: yae ist correct
Kit Clement
Premium Member
- Joined
- Aug 25, 2008
- Messages
- 1,626
- Location
- Champaign, IL, USA
- WCA ID
- 2008CLEM01
- YouTube
- Visit Channel
:tu
KongShou
Veteran
OK so is anyone here going to take the BMO?
Thats British Mathematical Olympiad, by the way. And it is kinda hard.
Thats British Mathematical Olympiad, by the way. And it is kinda hard.
angham
Regular
Yeah I qualified for bmo1, but not looking forward to it 
KongShou
Veteran
Yeah I qualified for bmo1, but not looking forward to it
have u got ur result already? yay so have i!
angham
Regular
For ukmt maths challenge? I got 97
angham
Regular
So I turns out my teacher made a mistake and I'm only doing kangaroo :/
TDM
Legend
I only did the challenge a week ago, so I haven't got my results yet. But I did the senior one when our year should still be doing the intermediate one. I missed out 6 questions :fp
TheNextFeliks
Veteran
My favorite number is \( i \). "That's not a real number!" My favorite real number is \( e \)
rj
Veteran
I like Tau. Easier to use than pi.
ThomasJE
Premium Member
I've done three UKMT's; and I've got to the Olympiad twice. And I got A* in maths in year 10.
TDM
Legend
Only got 88. Complete fail. Someone at school got 20 more than me. Where's :fp when you need it.
D
Deleted member 19792
Guest
I might do a trig course over the summer just for funzies (I will probably PHAIL) but the hardest so far is pre-cal
KongShou
Veteran
I got 100 and got into BMO. if i had a chance to check the answers then i would have qualified by more. oh well.
Which Olympiad?
Which Olympiad?
ThomasJE
Premium Member
http://www.ukmt.org.uk/individual-competitions/intermediate-mathematical-olympiad/
This one. I've also done the junior olympiad.
5BLD
Legend
I got 97 in thy senior, i made lots of errors as usual, where i go "yay this is so exciting i found a 3 line method" and forgot to divide by 2 or something
I'll take more care in the olympiad maybe which is in like a few days
KongShou
Veteran
ooh i got 100 in the senior, so close. I just qualified for BMO1. Did you get in too? I kinda ran out of time in the SMC. LOL
5BLD
Legend
Yeah well no one got higher so I probably am entered for it. I had about 10 mins left actually, but I kept going "yeah that looks right" while checking.
