Subsequences
Instructions
Use the dynamic applet to explore the definition of a subsequence. You can change the initial sequence but, more importantly, you should generate new subsequences (using the button) and show the subsequence (in relation to the original sequence) by dragging out new terms, n, in the original sequence.
Reflection Questions
For the given sequence, what can you conclude about the limit of the sequence and the limits of its different subsequences? Does your conclusion works for both monotonic and non-monotonic sequences? How to prove your conclusion?