Limits of Sequences and Infinite Series
by Anonymous
Change the common ratio to see where convergence, divergence, and oscillation part ways, and find when an infinite geometric series still adds up to a finite sum.
About this app
An interactive math app for exploring arithmetic and geometric sequences, sequence limits, and infinite geometric series. Adjust the first term, common difference, common ratio, and number of terms to see how values change, whether a geometric sequence converges, diverges, or oscillates, and how partial sums approach a finite limit when |r| < 1. Guided missions provide practice with key cases such as r = 1, r = −1, and r = −0.5.
Use cases
- High school students learning sequences and series
- Teachers demonstrating convergence, divergence, and oscillation
- Learners practicing arithmetic versus geometric sequences
- Reviewing the infinite geometric series formula
Features
- Switch between arithmetic and geometric sequence modes
- Adjust first term, difference, ratio, and displayed term count
- Explore geometric sequence behavior through visual term displays
- Compare partial sums with the infinite-series limit
- Complete guided missions covering sequence and series concepts