Let F(n) be the nth term (n∈N+) of the series. Then this sentence can be written in the following form:

F(0) = 0，F( 1)=F(2)= 1，F(n)=F(n- 1)+F(n-2) (n≥3)

Obviously, this is a linear recursive sequence.

The derivation method of the general formula: using the characteristic equation

The characteristic equation of linear recursive sequence is:

X^2=X+ 1

solve

X 1=( 1+√5)/2，，X2=( 1-√5)/2

Then f (n) = c1* x1n+C2 * x2n.

∫F( 1)= F(2)= 1

∴C 1*X 1 + C2*X2

C 1*X 1^2 + C2*X2^2

The solution is c1=1√ 5, C2 =-1√ 5.

∴ f (n) = (1/√ 5) * {[(1+√ 5)/2] n-[(1-√ 5)/2] n} (√ 5 stands for the radical number 5).