Mathematical Induction Q (1 Viewer)

[J0n]

Can someone tell me how to do this??

 

[KeypadSDM]

Now you've got me something to do over the weekend. Thank you

 

[Giant Lobster]

Holy moly hes gonna try!

hey J0n are u class of 04? Damn... judging by the questions/answers u give, i have a feeling ur gonna beat us all

 

[Grey Council]

nah, he is in Uni.

edit;
wtf, he joined up in august 2003. Maybe he IS in our grade. shite.

 

[Xayma]

Well I can get the first stage the next stages might take a bit though. Dam the last proof is hard.

 

[J0n]

Originally posted by Giant Lobster
hey J0n are u class of 04?

Yeah, i'm class of 04

 

[Grey Council]

oh shit.

*rushed out with a knife and chops J0n's head off*

however, you DO realise, of course, that they will never ask a question like that in the exam? Like, EVER?

 

[abdooooo!!!]

they will.

look at the file name... its only the first one... there is many more harder ones that he/she is doing.

 

[Xayma]

I can do up to prove true for 1/2(m+1)=k+1, since m is directly related to k its hard finding the difference between 1/2(m+1)=k and 1/2(m+1)=k+1. If you want Ill post up to that point

 

[OLDMAN]

Hi everyone, I promised myself not to get sucked into this( forum) this year. Maybe just this one question.

The sigma sum notation could be confusing, particularly when there is an embedded summation(see Q8 HSC2000) or product like this one. First thing you have to do is have a feel for the expression by expanding it out.

For m=7, expression is 1+{6/5+(6*4)/(5*3)+(6*4*2)/(5*4*1)} and indeed it is equal to 7,

Now for m, expression is 1+{[(m-1)/(m-2)+[(m-1)(m-3)]/[(m-2)(m-4)+...+[(m-1)(m-3)...4*2]/[(m-2)(m-4)...3*1]}

The question is prove 1+{ }=m.
Assume true, that is {}=m-1, prove true for m+2 ie.:

1+{(m+1)/m+[(m+1)(m-1)]/[m(m-2)+...+)+...+[(m+1)(m-1)(m-3)...4*2]/[m(m-2)(m-4)...3*1]}=m+1
Now notice that the expression in {} has a common factor (m+1)/m.... the rest should be easy.

 

[Xayma]

Can you do it that way, by changing m since the max thing is 1/2(m+1)?

 

[OLDMAN]

Xayma, the induction variable is m - introducing another variable k could be confusing.

 

[J0n]

Oh, thanks OLDMAN

 

[Giant Lobster]

omg class of 04 this guy's scary
prolly ruse or sbhs or somefin

 

[abdooooo!!!]

nah OLDMAN is scary... so old.

ruse nerds don't normally post here this early... only just before or after the hsc. because they need to study now...

 

[abdooooo!!!]

Originally posted by GuardiaN
ruse nerds don't post here at all. period. Neither do SBHS nerds. Yeah, sure, top 10 post, but the actual NERDS, the absolutely freaky ones, very rarely use this site. Its a very big co-incidence that the top'ers of extension 1 and 2 maths for 03 and 02 have both been visiting this site. Thats what I think so anyway.

they're here... mr 100.xx from ruse has over 500 posts and now offering tutoring. i wonder where i heard of the name yewon before... oh distinction course

and that math nerd from your school last year and all the olympiad students thats on here... they are the freaky ones.

 

[abdooooo!!!]

crap... ahhh... i forgot to delete them posts... stupid GuardiaN

edit: now thats better

 

[AGB]

i said stop it u retard......

 

[Grey Council]

lol, who were you talking to Abbdoooo?
*looks around, spots no-one*
wtf, your becoming crazy. Too much study, I think.

lol

 

[abdooooo!!!]

im talking to myself... ok. you fools.

someone should really make it so that you can't delete posts... umm... but i can do it as well.

GuardiaN man... that questions sucks... i can't do it.

have to learn more calculus...