Arithmetic progression: the general formula an=a 1+(n- 1)d, the first term a 1, and the tolerance d.
An = the nth term of ak+(n-k) d, where AK is the kth term. If a, a and b form a arithmetic progression, then A=(a+b)/22.
Sum of the top n items in arithmetic progression: Let the sum of the top n items in arithmetic progression be Sn, that is, Sn=a 1+a2+...+ An;
Then sn = na1+n (n-1) d/2 = dn 2 (that is, the quadratic power of n)/2+(a1-d/2) n;
There are also the following summation methods: incomplete induction, accumulation and inverse addition.
Geometric series: general formula: an = a 1 * q (n- 1) (i.e. qn- 1 power), where a 1 is the first term and an is the nth term.
An = a 1 * q (n- 1), am = a 1 * q (m- 1), then an/am = q (n-m),
Where an = am * q (n-m); If A, G, and B constitute a neutral term with equal proportion, then g 2 = ab (a, B, and G are not equal to 0); If m+n=p+q, am×an=ap×aq2.
Let a 1, a2, a3...an, the sum of the first n terms in the geometric series form the sum of the first n terms in the geometric series:
Sn = A 1+A2+A3...ansn = a 1+a 1 * Q+a 1 * Q 2+...A 1 * Q (n-2)+A65438+。
sn=a 1( 1-q^n)/( 1-q)=(a 1-an*q)/( 1-q)；
Q is not equal to 1, and Sn=na 1.
Q= 1。 There are generally five methods for summation: complete induction (that is, mathematical induction), cumulative multiplication, dislocation subtraction, sum in reverse order, and split term elimination: formula method, cumulative method, cumulative multiplication and undetermined coefficient method.