Proof by induction
Is my solution correct, also in terms of guessing the formula initially I had thought you would use the chained equations to spot some kind of pattern in terms of Xn and X(n+1) but realised it wasn't getting me anywhere.
So intuitively I considered powers, is there any steps I should have taken in my thought process to narrow down my 'guess' of formula?
So intuitively I considered powers, is there any steps I should have taken in my thought process to narrow down my 'guess' of formula?
(edited 1 year ago)
Original post by mqb2766
think your formula is correct though it should be xn = ... rather than xn+1.
I think the guess is a hint that subbing values in is the way to go as youve done.
I think the guess is a hint that subbing values in is the way to go as youve done.
My bad you're right I meant to write Xn,thanks
Original post by Student 999
So intuitively I considered powers, is there any steps I should have taken in my thought process to narrow down my 'guess' of formula?
Unfortunately, it's pretty much all intuition.
Usually, my first step is to simply write enough terms, until I hopefully "get" the pattern. Sometimes I could be writing up to like 10 or 20 terms to reach a reasonable hypothesis - MAT prep trained me well on being patient. (Note: I guess in a way that's part of doing science - recognizing patterns of the world and making hypothesis)
In this case, the numerator and the denominator are both powers of 2 minus something, which isn't an outrageously obscure pattern to spot, I'd suppose.
Quick Reply
Related discussions
- Recursion Q
- Proof by induction - general question - why prove n=1 works?
- Algebra help for proof by induction
- Question on proof by induction for Inductive Sequences
- Core pure maths Series question
- edexcel further maths core pure paper 1
- Proof by induction question
- Proof by induction question
- Tesco induction
- BMO 1993, Round 1, Question 3
- Ocr further maths core pure 2 5th june 2023
- As further maths discussion
- UKMT senior challenge
- Roots of Equations Further Maths Help
- How do I use proof by induction on this, specifically using f(k+1)-f(k)?
- Oxbridge Maths - Interview Questions
- Learning ahead in FM
- Fun top secret info, Spread to your friends/try the first three
- How should I go about preparing for the STEP Maths exam?
- Bmo 2023/24
Latest
Trending
Last reply 3 days ago
Did Cambridge maths students find maths and further maths a level very easy?Last reply 2 weeks ago
Edexcel A Level Mathematics Paper 2 unofficial mark scheme correct me if wrongMaths
71
Trending
Last reply 3 days ago
Did Cambridge maths students find maths and further maths a level very easy?Last reply 2 weeks ago
Edexcel A Level Mathematics Paper 2 unofficial mark scheme correct me if wrongMaths
71
