hey,guys,i'm practicing proofs .so, i'll be writing some proofs for the community to point out flaws, and many others to learn
this are all about the golden ratios. often written as
first is the power proof, i.e
where is the nth Fibonacci number, which is defined as
we see that it is satisfied at n=1,2. we know that
since it satisfies all three at n,n-1,n-2.it must satisfy for all number.
induction, hence proved.