Properties of a Divergent Geometric Series

Question

I.

In the series $$\sum_{n=1}^{\infty} 2(1.1)^{n-1}$$, the common ratio is $$1.1$$, which is greater than 1.

II.

A geometric series with a common ratio $$r$$ diverges if $$|r| > 1$$.

III.

Although the series diverges, its sum can be calculated using the formula $$S = \frac{2}{1-1.1}$$.

Which of the above statements are true?

| n | $$a_n = 2(1.1)^{n-1}$$ |
|---|------------------------|
| 1 | 2                      |
| 2 | 2.2                    |
| 3 | 2.42                   |
| 4 | 2.662                  |

Accepted Answer

I and II are true

Answer

I, II, and III are true

Answer

Only II is true

Properties of a Divergent Geometric Series

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