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Proof by induction
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Student 999
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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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So intuitively I considered powers, is there any steps I should have taken in my thought process to narrow down my 'guess' of formula?
Last edited by Student 999; 1 month ago
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skejrjoen
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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.
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.
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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Spelunker
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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?
So intuitively I considered powers, is there any steps I should have taken in my thought process to narrow down my 'guess' of formula?
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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