#number theory no. 11, 12
neat pewterBOT
bronze dagger
I think I saw you do a proof by induction earlier. This is straight-forward with induction.
bronze dagger
When you replace n with n+1 in the equation, you end up with F_2(n+1)
No
I must have misunderstood. What's your question?
Between questions 11 and 12, one of them is for sums that end with an even number and one is for sums that end with an odd number. It's intentional that you can't end in certain places in each sum.
bronze dagger
I forget: Do you know how induction works? For question 11, can you plug in n+1 and show me the equation you get?
bronze dagger
The third line, the one with the pink on it, is algebraically correct. You just have to factor the right side a little and use the Fibonacci relation.
bronze dagger
,rotate
bronze dagger
There's also the small matter of understanding how to write proofs. You should probably look it up on youtube or khan academy. You shouldn't be starting with the formula that you're trying to prove, though I did tell you that you need to look at it in order to understand what you're aiming for. Just start with the more complicated expression and work with it using the inductive hypothesis until you get to F_2(n+1)^2
bronze dagger
,rotate
dusky scaffoldBOT
