Infinite series is an important part of higher mathematics course, and it is also an important content of college students' mathematics competition. It is an indispensable tool for studying functions. It not only plays an important role in modern teaching methods, but also has a wide range of applications in a large number of applied sciences such as differential equations and numerical calculations. Studying how to use the knowledge points of infinite series to solve problems and its application in college students ' mathematics competitions will help students better understand and master the content, and also have certain reference value for teachers' teaching.

Yibing Lai. The Application of Infinite Series in College Students' Mathematics Competition. Academic Journal of Mathematical Sciences (2023) Vol. 4, Issue 4: 62-73. https://doi.org/10.25236/AJMS.2023.040410.

[1] Lu Xiaoqing. Some thoughts on infinite integrals and number series. Research on higher mathematics. 2023, 26 (03): 10-13. 

[2] Gu Rong. Discussion on the method of judging the convergence and divergence of infinite series. Sci-tech wind. 2022 (26): 7-9. 

[3] Li Yanwu, Wang Jiahuan. A counterexample to the convergence and divergence of any series. Journal of Zaozhuang University. 2021, 38 (02): 33-36. 

[4] Özgen H. Nedret. On Absolute Matrix Summability of Factored Infinite Series and Fourier Series. Numerical Functional Analysis and Optimization. 2023, 44(12): 1300-1308. 

[5] Heon Nikole; Mills Melissa. Comparing the Textbook with Professors’ Intended and Enacted Potential Intellectual Need for Infinite Series in Calculus II. Investigations in Mathematics Learning. 2023, 15(3): 169-185. 

[6] Zhao Lijun, Song Jie, Huang Duanshan. Advanced Mathematics (II). Beijing: Peking University Press. 2019. 

[7] She Zhikun. National College Students' Mathematics Competition Analysis Course (Non- Mathematics) (Volume II). Beijing: Science Press. 2023. 

[8] Pu Heping. College Students Mathematics Competition Tutorial. Beijing: Electronic Industry Press. 2015. 

[9] Zhao Lili. Several summation methods of constant series. Journal of Henan Institute of Education (Natural Science Edition). 2023, 32 (02): 50-54. 

[10] Wang Chengqiang. Analysis of the test points of infinite series of mathematics in the past five years. Research on higher mathematics. 202124 (03): 17-21. 

[11] Zhu Li. Convergence and Divergence of Infinite Product. Journal of Science, Teachers College. 2022, 42(04): 6-8. 

[12] Wang Fei, Liu Jia. On the convergence and divergence judgment and summation method of infinite series. Research on higher mathematics. 2021, 24 (03): 10-12, 40. 

[13] Li Yanwu, Wang Jiahuan. A counterexample to the convergence and divergence judgment of any term series. Journal of Zaozhuang University. 2021, 3 8

[14] Xu Xiujuan. Research on the determination method of convergence and divergence of arbitrary series. Mathematics learning and research. 2020 (03): 119. 

[15] Hu Haoyu. The summation method of infinite series. Education modernization. 2019, 6 (90): 173-175.