# Proof by induction

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#1
A level further maths.
Can't solve the following question
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#2
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2 weeks ago
#3
(Original post by cm49919)
What have you tried?
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#4
(Original post by RDKGames)
What have you tried?
I have proved that it's true for n=1 and assume it's true for n=k. Then I let n=k+1, not sure if it's correct or not.
Last edited by cm49919; 2 weeks ago
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2 weeks ago
#5
(Original post by cm49919)
I have proved that it's true for n=1 and assume it's true for n=k. Then I let n=k+1, not sure if it's correct or not.
It reads a bit awkward but you get the jist of it.

Point here is to be clear. You are assuming the result to be true for all

then

and sub in the hypotheses for before simplifying in the same way you did.
Last edited by RDKGames; 2 weeks ago
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#6
(Original post by RDKGames)
It reads a bit awkward but you get the jist of it.

Point here is to be clear. You are assuming the result to be true for all

then

and sub in the hypotheses for before simplifying in the same way you did.
Thank you so much
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2 weeks ago
#7
(Original post by cm49919)
Thank you so much
Note: Starting with n=1, the formula defines .

As such your base case needs to be for both and
Last edited by ghostwalker; 2 weeks ago
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