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- #1

The n+1 and n-1 should be smaller by the F but I dont know how to do that on a computer

Any help is appreciated

- Thread starter 06Rousher
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- Thread starter
- #1

The n+1 and n-1 should be smaller by the F but I dont know how to do that on a computer

Any help is appreciated

- Admin
- #2

\(\displaystyle A_{n}=F_{n+1}^2-F_{n-1}^2\)

So, as suggested, let's see if a pattern develops:

\(\displaystyle A_1=F_2^2-F_0^2=1^2-0^2=1=F_2\)

\(\displaystyle A_2=F_3^2-F_1^2=2^2-1^2=3=F_4\)

\(\displaystyle A_3=F_4^2-F_2^2=3^2-1^2=8=F_6\)

\(\displaystyle A_4=F_5^2-F_3^2=5^2-2^2=21=F_8\)

At this point, we could state the induction hypothesis $P_n$:

\(\displaystyle F_{n+1}^2-F_{n-1}^2=F_{2n}\)

Can you proceed?

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- #4

I mean can you continue the proof by induction. The hypothesis is what we notice appears to be the pattern that arises when computing the first several terms of the sequence we are asked to explore. Have you been using induction in your course?Proceed with continuing the pattern?

Im not understanding the hypothesis of F 2n aswell

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