Question

Determine whether each of the following statements about Fibonacci numbers is true or false.

a.) 𝐹𝑛+1 = 𝐹𝑛2 + 𝐹(𝑛−1)3 for every n ≥ 2

b.) 𝐹𝑛 = 2𝐹𝑛+1 for every n ≥ 2

Answer 1

Fibonacci series : 0,1,1,2,3,5,8,13...respective to f1,f2,f3,f4,f5

F_n+1=F_n2 + F_(n-1)3              n≥2

Simplify the equation

F_n+1= F_n2 +F_3n-3

Substitute n with 2

F₍₂₊₁₎=F_(2*2)+F_([3*2]-3)

We get

F₃=F₄+F_{3 ...}

which is false

 

b)

F_n=2F_n+1    where n≥2

F_n =2F_n+1

F₂=2F₂₊₁

F₂=2F₃…

Which is false