斐波那契数列 (一些公式)

 

gcd(2^x-1,2^y-1)=2^gcd(x,y)-1;

gcd(Fib[x],Fib[y])=Fib[gcd(x,y)];

Fbi[n]/Fbi[n+1]≈0.618  (n较大时，7开始就可）

Fib[1]+Fib[2]+Fib[3]+...+Fib[n]=Fib[n+2]-1;

Fib[1]^2+Fib[2]^2+Fib[3]^2+...+Fib[n]^2=Fib[n]*Fib[n+1];

Fib[1]+Fib[3]+Fib[5]+...+Fib[2*n-1]=Fib[2*n];

Fib[2]+Fib[4]+Fib[6]+...+Fib[2*n]=Fib[2*n+1]-1;

Fib[n]=Fib[m]*Fib[n-m+1]+Fib[m-1]*Fib[n-m];(n>=m)

Fib[n-1]*Fib[n+1]=Fib[n]*Fib[n]+(-1)^n;