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Series prerequisite for Proof by induction? (1 Viewer)
- Thread starter AKONS
- Start date
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: 
has n terms, whilsts the last term is 
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
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- Oct 21, 2019
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- HSC
- 2020
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.
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.
why?
That's all the knowledge you need before starting induction
Fair.
What's the reason?
Difficulty is relative.
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.
lol