Proof by induction

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Student 999
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#1
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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?Name:  Screenshot 2022-06-25 at 15.21.39.png
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Last edited by Student 999; 1 month ago
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skejrjoen
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god I’m so glad I don’t do maths
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mqb2766
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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.
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Student 999
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(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.
My bad you're right I meant to write Xn,thanks
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Spelunker
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math hard :confused:
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tonyiptony
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(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.
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