Mathematical Induction Q (1 Viewer)

[Grey Council]

nah nah, its applications of calculus to the physical world. It requires you to learn Growth and Decay. Don't worry, you'll soon be doing em. Its pretty easy, trust me, you'll ace it.

 

[pigs_can_fly]

actually, yewon is a girl

 

[Xayma]

Originally posted by OLDMAN
the induction variable is m - introducing another variable k could be confusing.

I see how it works now, I was getting confused before because I was thinking of the m in the equation as one variable and r as another when they are directly related. Ill try it again tomorrow.

 

[ND]

Originally posted by 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.

Ooo, welcome back. I'll be joining Isaac next year at macq (i decided not to go to my med interview).

 

[Grey Council]

oo, my favourite maths helper outer'er is back. Welcome back ND.

 

[abdooooo!!!]

Originally posted by pigs_can_fly
actually, yewon is a girl

and? yewon is an idiot enough said... oh the mr thing... miss ok?

 

[abdooooo!!!]

Originally posted by GuardiaN
nah nah, its applications of calculus to the physical world. It requires you to learn Growth and Decay. Don't worry, you'll soon be doing em. Its pretty easy, trust me, you'll ace it.

yeah man. i have to or else... shit... my hsc is gone. LOL

 

[OLDMAN]

ND : Yes Isaac is rarin to swap car stories with you. Congrats and good luck.

 

[KeypadSDM]

This is a really wierd one. If you look at it, the sum for m=k and m=k+2 are identical in form (With a little rearranging), and if you assume true for m=k, then it's true for m=k+2.

I don't get it... I need to work on my sigma induction proofs.

 

[Grey Council]

Didn't oldman solve it already?

 

[ND]

Originally posted by GuardiaN
oo, my favourite maths helper outer'er is back. Welcome back ND.

Not exactly (i just check my email and a couple of BoS forums every few days). Who in their right mind would pay $2000 for a plane ticket and only stay away for 1 week.

ND : Yes Isaac is rarin to swap car stories with you. Congrats and good luck.

Heheh. Thanks.