Let Fn be the nth Fibonacci number Prove by induction on n t

Let Fn be the nth Fibonacci number Prove by induction on n that, for all n >=1, k=1, F2k-1 = F2n.

Solution

What you are trying to prove is wrong.

Because for k = 1, F_2k-1 = F₁.

And F₁ = 1 in Fibonacci sequence.

And since F_2n is always greater than or equal to F₂ for n >= 1, that is

F_2n >= F₂ = F₁ + F₀ = 2 for n >= 2.

Therefore, F_2k-1 F_2n for k =1 and n >= 1.