APFIVE Properties Of Geometric Series
All of the following statements about geometric series are true except:
| n | S_n |
|---|---|
| 1 | 0.5 |
| 2 | 0.75 |
| 3 | 0.875 |
| 4 | 0.9375 |
A
For a convergent geometric series, the sum is given by $$S = \frac{a}{1 - r}$$ where $$a$$ is the first term.
B
A geometric series converges if $$|r| < 1$$.
C
If the partial sums of a geometric series grow without bound or oscillate, the series diverges.
D
A geometric series converges if $$|r| \geq 1$$.
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