1. Find the sum of the infinite geometric series $16 + 4 + 1 + \ldots$. If the sum is a fraction, write it in the form a/b. The sum is ___.
2. Which of the following infinite geometric series has a finite sum?
3. Write the repeating decimal $0.\overline{4}$ as a fraction in simplest form. The fraction is ___.
4. Calculate the sum of the infinite geometric series $8 - 4 + 2 - 1 + \ldots$. If the sum is a fraction, write it in the form a/b. The sum is ___.
5. An infinite geometric series diverges and does not have a sum if the absolute value of its common ratio $r$ is...
6. Use an infinite geometric series to convert the repeating decimal $0.\overline{8}$ to a fraction in simplest form. The fraction is ___.
7. When converting the repeating decimal $0.\overline{789}$ to a fraction using an infinite geometric series, what is the value of the common ratio $r$?
8. Convert the repeating decimal $0.\overline{12}$ into a fraction. Your answer should be in simplest form: ___.
9. Convert the repeating decimal $0.2\overline{3}$ into a fraction in simplest form. The result is ___.
10. To convert $0.4\overline{1}$ to a fraction, you write it as $0.4 + 0.0\overline{1}$. What is the first term $a$ of the infinite geometric series for the repeating part, $0.0\overline{1}$?