1. When the common ratio of geometric progression is equal to 1, the sum formula of the first n terms of geometric progression is: Sn=na 1.

2. When the common ratio of geometric progression is not equal to 1, the sum formula of the first n terms of geometric progression is sn = a 1 (1-qn)/(1-q), where a1is the first term and q is the common ratio.

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Formula derivation is a mathematical method used to prove the correctness of mathematical formulas or theorems. This is a process of logical reasoning. Through the known mathematical principles and formulas, new formulas or theorems are gradually derived. Formula derivation has important application value in mathematics, which can help us to deeply understand mathematical concepts and principles and establish a more complete and rigorous mathematical knowledge system.

The process of formula derivation is generally divided into determining known conditions and objectives: before derivation, it is necessary to clarify known mathematical conditions and objectives to be proved. These conditions may include known formulas, theorems or definitions. The goal is a formula or theorem that needs to be proved. Establish a logical relationship: According to the known conditions and goals, we need to establish a logical relationship between them.

This is usually achieved through observation, analysis, induction and other thinking processes. In this process, we need to find out the connection and difference between the known conditions and the target, so as to determine the direction and thinking of derivation. Step-by-step derivation: after determining the logical relationship, it needs to be deduced step by step. This process usually requires the use of known formulas, theorems or definitions, and reasoning and deformation according to logical relations.

In the process of derivation, we need to pay attention to the basis and rationality of each step to ensure the rigor and correctness of the derivation process. Draw a conclusion: When all the derivation steps are completed, we can draw a conclusion. This conclusion is the formula or theorem that we need to prove. In order to ensure the correctness of the conclusion, we need to re-examine the whole derivation process to ensure that there are no mistakes and omissions. When deriving the formula.

We should pay attention to fully understanding the known conditions and objectives: only by deeply understanding the known conditions and objectives can we clarify the direction and thinking of derivation and avoid detours. Master basic mathematical principles and methods: Formula derivation needs to use basic mathematical principles and methods, such as multiplication and distribution law, Pythagorean theorem, calculus and so on. Only by mastering these basic knowledge can we perform better.

Pay attention to the rigor of logical relationship: Formula derivation needs rigorous logical relationship, and every step of reasoning needs basis and rationality. In the process of derivation, we need to pay attention to the logical relationship of each step to ensure correctness. Apply what you have learned: Formula derivation not only needs to prove the correctness of a formula or theorem, but also needs to understand the mathematical ideas and principles behind it. Draw inferences from others and apply what you have learned.

You can apply what you have learned to solving practical problems and improve your mathematics literacy and ability. In a word, formula derivation is an indispensable part of mathematics learning. By mastering the methods and skills of formula derivation, we can better understand the concepts and principles of mathematics and improve our mathematical thinking ability and problem-solving ability.