Two classics from a century ago, with a great variety of unsolved exercises:
Theorie und Anwendung der unendlichen Reihen, by Konrad Knopp (1922) --- English translation
An Introduction to the Theory of Infinite Series by Thomas Bromwich (1908)
An older but more elementary text is Introduction to Infinite Series by William Osgood (1897)
An exercise from Knopp:
An exercise from Bromwich:
An exercise from Osgood:
