# Limit series

An infinite series, or just series here since almost every series that we'll be looking at will be an infinite series, is then the limit of the partial sums. Or. As the positive integer n {\displaystyle n} n becomes larger and larger, the value n ⋅ sin ⁡ (1 n) {\displaystyle n\cdot \sin {\bigg (}{\frac {1}{n}}{\bigg)}}  ‎History · ‎Real numbers · ‎Metric spaces · ‎Topological spaces. Define series limit: the position (as of a wavelength, wave number, or frequency) in an atomic line spectrum toward which the series progresses in the.