# Limit series

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. Infinite series are defined as the limit of the infinite sequence of partial sums. Since we already know how to. These images, in the form of lines, appear to have a regularity in spacing, coming closer together toward the shortest wavelength, called the series limit. The links for the page you are on will be highlighted so you can easily find them. A Cauchy sequence is a sequence whose terms ultimately become arbitrarily close together, after sufficiently many initial terms have been discarded. If it converges determine its sum. Mathematics Stack Exchange works best with JavaScript enabled. This interdependence causes each player to consider Since this series converges we know that if we multiply it by a constant c its value will also be multiplied by c. Take a look at this picture for example:.

### Limit series Video

Limit of a Series The limit of the sequence terms is,. Calculus II [ Notes ] [ Practice Problems ] [ Assignment Problems ]. Now, since the main topic of this section is the convergence of a series we should mention a stronger type of convergence. In the previous section we spent some time getting familiar with series and we briefly defined convergence and divergence. Studying for a test? The divergence test is the first test of many tests that we will be looking at over the course of the next several sections. Integral Test [ Notes ] [ Practice Problems ] [ Assignment Problems ]. This would be the sum of the first 2 terms. Absolute Convergence [ Notes ] [ Practice Problems ] [ Assignment Problems ]. In the previous section we spent some time getting familiar with series and we briefly defined convergence and divergence. If the series terms do not go to zero in the limit then there is no way the series can converge since this would violate the theorem. Infinite series as limit of partial sums. Convergent and divergent sequences.