$a_{n} \to 0 \Rightarrow \sum{}a_{n}$ converges

No — it is false.

Go deeper· Explained in full in Series tests — decision tree and the trap list· Asked in CSIR NET December 2025· From The Real Line › Series: comparison, ratio, root, Raabe, condensation, alternating, rearrangements

Published 23 Aug 2026. Found a mistake? Tell us — corrections are the fastest thing we act on.