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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


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 , 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


9. The Divergence Test says that the series


10. The series

may converge, but more investigation is needed