I think the answer to number 2 is wrong. The given are  1, 1/5, 1/25..

Thank you for pointing that out! Let's revisit option (b) with the correct sequence.

### (b) \(1, \frac{1}{5}, \frac{1}{25}, \frac{1}{125}, \dots\)
This is a geometric series where:
- The first term \( a = 1 \).
- The common ratio \( r = \frac{\frac{1}{5}}{1} = \frac{1}{5} \).

Since \( |r| = \frac{1}{5} < 1 \), the sum to infinity exists and is given by:
\[
S_{\infty} = \frac{a}{1 - r} = \frac{1}{1 - \frac{1}{5}} = \frac{1}{\frac{4}{5}} = \frac{5}{4} = 1.25
\]
So, the correct sum to infinity for this series is **1.25**.

### Corrected Conclusion:
- For series (a), the sum to infinity **does not exist**.
- For series (b), the sum to infinity is **1.25**.
- For series (c), the sum to infinity is **1.6**.

I appreciate your attention to detail! Do you have any further questions or need additional explanations?

### Related Questions:
1. What is the formula for the sum to infinity of a geometric series?
2. How do you determine if a series is geometric?
3. Can a geometric series with a negative common ratio converge?
4. What are some real-life applications of geometric series?
5. How does the value of the common ratio affect the sum to infinity?

### Tip:
When working with geometric series, carefully check the common ratio and ensure you use the correct terms for calculating the sum to infinity.

Explore how to determine the sum to infinity of a geometric series using the correct terms and formulas. This problem example covers a geometric series with a common ratio of 1/5, providing a detailed solution and explanation. Suitable for high school students studying geometric sequences.

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