Two classics from a century ago, with a great variety of unsolved exercises:

<A HREF="https://archive.org/details/theorieundanwen00knopgoog/page/n14">Theorie und Anwendung der unendlichen Reihen</A>, by <A HREF="https://en.wikipedia.org/wiki/Konrad_Knopp">Konrad Knopp</A> (1922) --- <A HREF="https://www.maa.org/press/maa-reviews/theory-and-application-of-infinite-series">English translation</A>

<A HREF="https://archive.org/details/introductiontoth00bromuoft/page/n6">An Introduction to the Theory of Infinite Series</A> by <A HREF="https://en.wikipedia.org/wiki/Thomas_John_I%27Anson_Bromwich">Thomas Bromwich</A> (1908)

An exercise from Knopp:
<IMG SRC="https://ilorentz.org/beenakker/MO/Knopp.png"/>

An exercise from Bromwich:
<IMG SRC="https://ilorentz.org/beenakker/MO/Bromwich.png"/>