Extension Mathematics: Induction (1 Viewer)

[beve]

This ones a bit too curly for my (lack of) mathematical abilities, one of the steps in the prove true for n=k+1 section is throwing me off so can someone take me from start to finish?

1/(1x2) + 1/(2x3) + 1/(3x4) ... + 1/n(n+1) = 1 - 1/(n+1)

 

[beve]

Ive substituted it in but I don't understand how to get to the next part of it.

 

[minijumbuk]

S_k+1 = S_k + T_k+1

So you gotta prove that:
1- 1/(k+2) = 1-1/(k+1) + 1/(k+1)(k+2)

RHS = (k+1-1)/k+1 + 1/(k+1)(k+2)
= (k(k+2)+1)/(k+1)(k+2)
= (k² + 2k + 1) / (k+1)(k+2)
= (k+1)/(k+2)
= (k+2-1)/(k+2)
= 1 - 1/(k+2)
= LHS #

Therefore true for n=k+1.

 

[beve]

Cheers.

 

[Devouree]

wow, thanks minijumbuk!! I've been having problems understanding that step as well. Most textbooks just tell you to write a template that I can never get...

@ beve: Your school must be pretty far in front of other schools, as Maths induction in Fitzpatrick is 3U around page 60~70 (I think...), and for Cambridge is 3U Chapter 6N or something similar. The only school I know whose grade is up to this is Sydney Grammar, and I think they don't do 2U or something...

 

[beve]

wow, thanks minijumbuk!! I've been having problems understanding that step as well. Most textbooks just tell you to write a template that I can never get...

@ beve: Your school must be pretty far in front of other schools, as Maths induction in Fitzpatrick is 3U around page 60~70 (I think...), and for Cambridge is 3U Chapter 6N or something similar. The only school I know whose grade is up to this is Sydney Grammar, and I think they don't do 2U or something...

Maybe, but our class has 4 people in it. So maybe it moves faster than other extension classes around.

I still suck lol.