Good day, I wanted to ask the experts what books containing various methods for calculating series they can recommend.I am a bachelor and am preparing for student olympiads in mathematics. While studying integrals, I came across an amazing book by Paul J. Nahin Inside Interesting Integrals https://www.amazon.com/Inside-Interesting-Integrals-Substitutions-Undergraduate/dp/1493912763.And now I'm looking for something similar for series calculus.
Many thanks.
I will leave here the books that seemed good to me.
First, a good textbook/problem book is the Real Infinite Series by Daniel D. Bonar (Author), Michael J. Khoury Jr. (Author) https://www.amazon.com/Infinite-Mathematical-Association-America-Textbooks/dp/0883857456 . The book is excellent both for studying theory and for consolidating practice. There you can find basic concepts and methods for working with series for beginners, as well as subtle points of interest for advanced students. The book is very conveniently divided into chaptersIn chapter 5 you will find a collection of problems in rows from the Putnam Olympiads.And I would like to highlight the list of references in this book, I advise everyone to read it, there are only diamonds
Puthnam and Beyond https://www.amazon.com/Putnam-Beyond-Razvan-Gelca/dp/0387257659 This book is not entirely in series, but there are enough series in it. There are many problems, for each problem there is a detailed solution.