Book recommendation for techniques of evaluating Series?

Al-Layth · Jun 1, 2023

TL;DR Summary: I am looking for a good thorough book that is devoted to assembling and explaining techniques of evaluating series.

evaluating series is a very big problem for me right now. I know nowhere near as much about it as I do integration, and the main reason for this is that its quite easy to find detailed books devoted to techniques in integral calculus. But I can hardly find anything for series.

please recommend me something, the more comprehensive the better. I like books that do one specific thing very thoroughly.

fresh_42 · Jun 1, 2023

Al-Layth said:

TL;DR Summary: I am looking for a good thorough book that is devoted to assembling and explaining techniques of evaluating series.

evaluating series is a very big problem for me right now. I know nowhere near as much about it as I do integration, and the main reason for this is that its quite easy to find detailed books devoted to techniques in integral calculus. But I can hardly find anything for series.

please recommend me something, the more comprehensive the better. I like books that do one specific thing very thoroughly.

https://www.amazon.com/dp/B00OUR06EO/?tag=pfamazon01-20

has both.

FactChecker · Jun 1, 2023

There are a million tricks for summing up a million different series. There are extensive books of tables and online tools. You might want to reconsider spending a lot of time on those tricks when there are so many fundamental mathematical subjects to learn. IMHO, only a handful of the tricks are worth learning.
But, to each his own.

PS. I have the same opinion of integration techniques.

MidgetDwarf · Jun 9, 2023

Al-Layth said:

TL;DR Summary: I am looking for a good thorough book that is devoted to assembling and explaining techniques of evaluating series.

evaluating series is a very big problem for me right now. I know nowhere near as much about it as I do integration, and the main reason for this is that its quite easy to find detailed books devoted to techniques in integral calculus. But I can hardly find anything for series.

please recommend me something, the more comprehensive the better. I like books that do one specific thing very thoroughly.

Are you struggling with series in the context of a calculus class, or real analysis class?

Truth be told, the most common techniques for book style problems are the Geometric Series Test, P-Series Test, Ratio Test, Root Test, Divergence Test, Comparison Test, and I may be missing a few.

The trick with series is first understanding what a sequence is, convergence of sequence, what a series is, and convergence of a sequence.

haushofer · Jun 10, 2023

Simply Stewart's Calculus book?

Book recommendation for techniques of evaluating Series?

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