1, dislocation subtraction

This kind of problem is often used in the new series composed of arithmetic and ratio. We should distinguish the two terms, and at the same time use equal ratio and unify the number of intermediate terms.

2. Cracks cancel each other out

Its problem-solving type lies in fractional sequence, and all intermediate directions are eliminated after deformation. If there are many powers of negative one, it is possible that the number of intermediate terms will increase or decrease at this time, which can also be eliminated.

3. Add in reverse order

The classical application of reverse addition lies in the application of summation formula of arithmetic sequence. Using the properties of arithmetic progression, we can get arithmetic progression's summation formula, which can also be said to be the proof of the summation formula of arithmetic sequence.

4. Group summation

Group summation is often the sum of 2n terms, or the sum of multiple terms. This kind of problem is often the arithmetic difference of n terms and the ratio of n terms, which can be solved separately by using the summation formula of arithmetic difference and ratio series.

It is difficult to scale and solve the range of a certain value. For example, scaling is the summation of series, and the final summation needs to be proved by proving inequality. When solving the range of a certain value, it is necessary to sum first, and then judge the solution method according to the known conditions of the topic.

Data expansion:

Solve the difficult line series scaling first: Why are these problems difficult to solve? The reason is simple, we must maintain a proper balance and justice! If you can't have a strong mathematical problem-solving idea, you can only be in a fog. The key lies in the transformation between variant form and result. The best way to answer this question is to reason step by step from back to front, so that the goal is clear enough!

If we can't sort out the variant forms according to the results, then the sense of direction will be lost, and the solution to the scaling problem of series will be difficult to prove, so students must be clear about this. However, there are really too many ways to find the general term of a series. We can solve the general term by defining or modifying the given relationship.

For example, two sides take reciprocal and logarithm at the same time, or two sides divide by a term according to the specific form of the equation to construct a new series to indirectly solve the original series.