2. Reverse addition: This method is suitable for the summation of some specific forms of series, such as arithmetic progression summation. The specific operation is to add the first item and the last item of the series in pairs, then pair the middle items in turn, and finally add all the paired sums to get the sum.
3. Dislocation subtraction: This method is applicable to the series of An=Bn multiplied by Cn, where Bn is arithmetic progression and Cn is geometric progression. First, list the first n terms and Sn of the series, then multiply Sn by the common ratio Q of geometric series, and then subtract it from the original Sn dislocation to get the sum of the series.
4. Splitting elimination method: This method is suitable for a series that can be decomposed into two or more parts. By decomposing each term of a series into several parts, the summation process is simplified by using the mutual cancellation properties of these parts.
5. Group summation method: This method divides the series into several groups, and the items in each group have the same characteristics, and then sums each group separately.
6. Mathematical induction: This is a summation method based on recursive nature. By proving that the sum of the first n terms of a series satisfies a certain recurrence relation, the sum formula of the series is gradually derived.
7. Observation method: This method relies on the intuitive understanding and analysis of the characteristics of the sequence, and directly obtains the summation formula by observing the regularity of the sequence.