Book recommendation for techniques of evaluating Series?

In summary, the book has extensive coverage of the different techniques for evaluating series. However, it is not the best book for someone just starting out.
  • #1
Al-Layth
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4
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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  • #2
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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  • #3
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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  • #4
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.
 
  • #5
Simply Stewart's Calculus book?
 

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