Considering the Fibonacci sequence how does F with subscript 1+2+3+4+5 = 610?

Guest Nov 13, 2014

#1**+10 **

F(1+2+3+4+5) = F(15) = 610

BTW.......we can calculate any Fibonacci number with index "n" using this formula....

[Phi^{n} - (-Phi)^{-n} ] / √5 ....where Phi = [ 1 + √5 ] / 2

The odd thing about this "formula" is that it looks as though it should produce some irrational number........but it doesn't !!!!

Try the formula with n = 15 and see if it doesn't give you 610.......

CPhill
Nov 13, 2014

#1**+10 **

Best Answer

F(1+2+3+4+5) = F(15) = 610

BTW.......we can calculate any Fibonacci number with index "n" using this formula....

[Phi^{n} - (-Phi)^{-n} ] / √5 ....where Phi = [ 1 + √5 ] / 2

The odd thing about this "formula" is that it looks as though it should produce some irrational number........but it doesn't !!!!

Try the formula with n = 15 and see if it doesn't give you 610.......

CPhill
Nov 13, 2014