Good book for analysis in particular sequences and series

Question

I’m currently studying pure mathematics and I’m finding the analysis sections quite difficult to digest from the course text books. Could anybody recommend some good textbooks that explain sequence and series well in particular finding if they are convergent or divergent.

Thanks

Answer 1

Problems in Mathematical Analysis I: Real Numbers, Sequences and Series. It's a brilliant book. Basically focused on problem solving skills. If you read this book you will have good skills in problem solving in real analysis.

Answer 2

Two recommendations:

• The highly readable classic Theory and Application of Infinite Series by Konrad Knopp is too good to be mentioned in the comment section only. I appreciate his style providing a wealth of information for the beginner in an elaborate, gentle wording but never being lengthy.

• Another very nice book is Real Infinite Series by D.D. Bonar and M. J. Khoury. The authors provide besides all basic convergent tests also some more sophisticated techniques. They present in chapter 4 $107$ gems of interesting series and discuss in chapter 5 series problems and solutions from the Putnam competitions. I also like Appendix A with $101$ True or False questions and Appendix C containing many interesting references.