1, arithmetic progression is a common series. If a series starts from the second item, the difference between each item and its previous item is equal to the same constant. This series is called arithmetic progression, and this constant is called arithmetic progression's tolerance. The tolerance is usually expressed by the letter D. For example, 1, 3,5,7,9 ... (2n-/kloc. The general formula of arithmetic progression is: an = a1+(n-1) D. The sum formula of the first n terms is: sn = n * a1+n (n-1) d/2 or sn = n (a/kloc-). Note: All the above n are positive integers.

For example, the tolerance of 65438 series +0, 3, 5, 7, ..., 97, 99 is d=3- 1=2, which will be extended to:

A 1, A2, A3...an, n = odd, sn = (a ((n-1)/2)) * ((n-1)/2).

2. The essence of the split term method is to decompose each term (general term) in the sequence, and then recombine it, so that some terms can be eliminated, and finally the purpose of summation can be achieved. The relationship between multiples of general term decomposition (split term).

Example 1 Find the sum of the first n terms of the sequence an= 1/n(n+ 1) by using the basic form of fractional split terms.

Solution: an =1/[n (n+1)] = (1/n)-[1/(n+1)] (crack term)

Then sn =1-(1/2)+(1/2)-(1/3)+(1/4) ...+.

= 1- 1/(n+ 1)

= n/(n+ 1)