#mathematical induction proof question
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compact viper
Because 1 + ... + (2n - 1) = P(n), which we've established to be n^2.
summer dawn
Because 1 + ... + (2n - 1) = P(n), which we've established to be n^2.
Ik P(n)=1+3+5+...+2n-1 the why they replaced it with an 2n+1
compact viper
Ik P(n)=1+3+5+...+2n-1 the why they replaced it with an 2n+1
Because that's the point of induction.
We suppose that the formula for P(n) works and show that it also works for P(n + 1).
summer dawn
Because 1 + ... + (2n - 1) = P(n), which we've established to be n^2.
I thought it should be for P(n+1) P(n)=1+3+5+...+2n-1= n^2 + (n+1)
And that's all idk where they goy the 2n+1 from?
compact viper
I thought it should be for P(n+1) P(n)=1+3+5+...+2n-1= n^2 + (n+1)
And that's al...
Well, because 2n + 1 is the next odd number after 2n - 1.
So, if P(n) = 1 + 3 + ... + (2n - 1), then P(n + 1) = 1 + 3 + ... + (2n - 1) + (2n + 1).
summer dawn
Well, because 2n + 1 is the next odd number after 2n - 1.
So, if P(n) = 1 + 3 + ...
Got it ty btw do u recommend me anything that would help me learn proving by induction coz I'm really bad at it and at proofs in general
lapis flumeBOT
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