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Series: A Series of Seriously Simple Series Questions True or False

1. Which of the following are series?

(i) 3

(ii) 3 + 4

(iii) 3,4 -> (i) and (ii)

2. -> 14
3. Determine which series has expanded form


4. Find the first 3 terms of the sequence of partial sums for the series

. -> 0,3,6

5. The infinite sequence  has partial sums Sn given by the formula

Which of the following statements must be true? ->  converges to 0.

6. Consider the infinite series  and the following statements:

(I) If  converges then .
(II) If the terms an converge to 0 then  converges.
(III) If the terms an do not converge to 0 then  diverges.

Which statements must be true? -> (I), (II), and (III)

7. If  diverges, what can we say about the behavior of ? -> We can't say anything about the behavior of .
8. The Divergence Test says that the series

-> diverges

9. The Divergence Test says that the series

-> converges

10. The series

-> may converge, but more investigation is needed