APFIVE Properties of Series Convergence
I. The series $$\sum_{n=1}^\infty \frac{1}{n^2}$$ converges.
II. The series $$\sum_{n=1}^\infty \frac{1}{n}$$ converges.
III. The Alternating Harmonic Series $$\sum_{n=1}^\infty (-1)^{n+1} \frac{1}{n}$$ converges conditionally.
Which of these statements are true regarding series convergence?
| n | Partial Sum s_n |
|---|---|
| 1 | 1.0 |
| 2 | 0.5 |
| 3 | 0.833 |
| 4 | 0.583 |
| 5 | 0.783 |
A
I and III only
B
I, II, and III
C
II only
D
I only
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