Sequences

Where does a list end up?

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• $a_n \to L$: for every $\varepsilon > 0$ there's an $N$ with $|a_n - L| < \varepsilon$ for all $n \ge N$.
• Bounded sequences can fail to converge, like (−1)ⁿ.
• An increasing sequence with an upper bound always converges (monotone convergence).

Steps

1. Halving forever
2. Converging sequences
3. Find N
4. Flip-flop
5. Leading terms
6. Always growing, never escaping