●●● ●●●● ●●●●● ●●●● ●●0●● Fibonacci Numbers ●●●0 ●●●● n1+Fn2;F0=0;F1 0,1,1,2,3,5,8,13,21,34,55, …=-061803 ●C| osed form 1+√5 Fn=() 2 2)/5 It can easily proved by mathematical induction ● Golden ratio 161803 o Fibonacci numbers grow exponentially10 ⚫ Fn = Fn-1 + Fn-2 ; F0 = 0; F1 = 1 ⚫ 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, … ⚫ Closed form: ⚫ It can easily proved by mathematical induction. ⚫ Golden ratio: ⚫ Fibonacci numbers grow exponentially. Fibonacci Numbers 1 5 1 5 (( ) ( ) ) / 5 2 2 n n F n + − = − 1 5 1.61803 2  + = = = -0.61803…