Series prerequisite for Proof by induction? (1 Viewer)

AKONS

Active Member
Hi guys!

I'm very aware this sounds like a noob question but are series and sequences (such as arithmetic or geometric) required to be already learnt, for a student to be able to learn proof by induction?

cossine

Member
Not really.

As such you should study series before induction.

Qeru

Well-Known Member
Nope no need for AP and GP, but you definitely need to understand what a 'sequence,' and what a 'series' is. It may also be wise to understand how the number of terms of a series and the last term of a series can both depend on a variable. For example the series: $\bg_white 1^2+2^2+3^2+...+n^2$ has n terms, whilsts the last term is $\bg_white n^2$ so if we had 3 terms the last term would be 9 if we had 4 terms the last term would be 16 etc. You should also touch up on recursive series.

Time&moretime

Active Member
Yes it is highly encouraged for students to be able to recognise patterns of numbers as taught in sequences and series as a means of being able to tackle proof by induction more easily. The range of methods of induction in the extension 2 course are wide, however to my knowledge I know that some of these methods require the ability to recognise number patterns quickly that come under the arithmetic and geometric category. These are taught in sequences and series. Hope this helps.

A1La5

New Member
It definitely can be a helpful prerequisite for mathematical induction but it's not completely necessary to understand series if you want to do induction. My school, for instance, covered induction first without going over series and sequences. I can do most induction problems to a decent standard despite me not having learned series yet.

tito981

Active Member
series and sequences is easy enough to finish in a couple hours, so i say just learn series and sequences first.

YonOra

Well-Known Member
Some harder Q's i've seen from HSC past papers will incorporate the best of both worlds. But no, not really.

vishnay

Member
Just google the definition of 'series' and 'sequences' and you're good.

YonOra

Well-Known Member
Just google the definition of 'series' and 'sequences' and you're good.
why?

vishnay

Member
That's all the knowledge you need before starting induction

YonOra

Well-Known Member
It's the first chapter in every book in history for a reason...

vishnay

Member
It's the first chapter in every book in history for a reason...
What's the reason?

YonOra

Well-Known Member
It's the easiest topic

vishnay

Member
Either way, difficulty isn't even a factor that contributes to series and sequences not being a pre-requisite for induction. You simply need to understand what a series is to do the series induction part of induction. 95% of induction questions (3U and 4U) can be attempted with a half-assed knowledge of 2U series and sequences.