1. Section 10.2 Sequences

2. In mathematics, a sequence is an ordered list of objects (or events). Like a set, it contains members (also called elements or terms), and the number of terms (possibly infinite) is called the length of the sequence. Unlike a set, order matters, and exactly the same elements can appear multiple times at different positions in the sequence. A sequence is a discrete function.mathematicssetmembers discretefunction In this course we will only be interested in infinite sequences with a rule for generating the terms (range values) and using the set of whole numbers or counting numbers as the domain.

3. Don’t let the new notation confuse you… Other notation:

5. The car converged to the tree. Some oscillating sequences never settle down to approach a single number.

6. Step 1: line up the most reasonable domain #’s. 0 1 2 3 … The numerators are all 1’s. The denominators are all powers of “2”. If we started with n=1…

7. Ex: #20 (read the directions) Final answer: this sequence converges to zero by the Squeeze Theorem.

8. Ex: #30 Use L’Hopital’s Rule L’Hopital again… One more time! This sequence converges to zero.

9. Ex: #38 Don’t forget to anti-

10. Ex: #44 (read the directions) Sequence mode is way too slow at creating tables…so let’s switch back to function mode!

11. Ex: #50