1. In this section, we will begin investigating infinite sums. We will look at some general ideas, but then focus on one specific type of series.

3. For example:

4. 1. Which series sum to a finite number? 2. How do we find/approximate such sums? 3. Which series blow up to ? 4. Which series diverge without blowing up to ?

6. Let be the sequence of partial sums. The series converges if the sequence converges. The series diverges if the sequence diverges.

7. Show that the given converges by finding an algebraic formula for.

8. Finding an algebraic formula for is not, in general, easy to do. Thus, determining the convergence/divergence of a series is not, in general, easy to do either. For a certain, very special, type of series, these questions are significantly easier.

11. If, the geometric series converges to. If the sum does not start at k = 0, then the limiting sum is. If a ≠ 0 and, the series diverges.

12. Determine whether the given series converges or diverges. If it converges, give the sum. If it diverges, find N so that S N ≥ 1000.

16. If, then diverges. NOTE: If, we can say nothing about the convergence or divergence of.

17. diverges because. diverges even though.