General term formula
an=a 1+(n- 1)d
an = Sn-S(n- 1)(n & gt; =2)
Sum of the first n terms
sn = n(a 1+an)/2 = n * a 1+n(n- 1)d/2
2. Equal ratio series
General term formula
an=a 1q^(n- 1)
an = Sn/S(n- 1)(n & gt; =2)
Sum of the first n terms
When q≠ 1, the formula of the sum of the first n terms of the geometric series is
sn=a 1( 1-q^n)/( 1-q)=(a 1-an*q)/( 1-q)(q≠ 1)
3. Fibonacci series
General term formula
an=( 1/√5)*{[( 1+√5)/2]^n-[( 1-√5)/2]^n}
Sum of the first n terms
sn =( 1/√5)*[( 1+√5)/2 )^(n+2)-[(( 1-√5)/2 )^(n+2)]- 1
4. Dayan series
General term formula
an=(n^2- 1)/2(n = 2k- 1,k∈N)
an=n^2/2 (n=2k,k∈N)
Sum of the first n terms
sn =(N- 1)(N+ 1)(2n+3)/ 12(N = 2k- 1,k∈N)
sn = N(N+2)(2n- 1)/ 12(N = 2k,k∈N)