Book recommendation for techniques of evaluating Series?

AI Thread Summary
A user seeks a comprehensive book focused on techniques for evaluating series, expressing frustration over the lack of resources compared to integral calculus. They emphasize the importance of thorough explanations and specific techniques, as evaluating series is currently a significant challenge for them. Suggestions include exploring common convergence tests like the Geometric Series Test and Ratio Test, while also considering foundational concepts like sequences and convergence. The discussion highlights the need for targeted learning materials in this area. Overall, finding a detailed resource on series evaluation is crucial for improving understanding.
Al-Layth
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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.
 
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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.
 
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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.
 
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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.
 
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