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Lesson 4: Finding Sums of Infinite Geometric Series — Practice Questions

  1. 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. 2. Which of the following infinite geometric series has a finite sum?

    • A. 1 + 3 + 9 + ...
    • B. 10 - 5 + 2.5 - ...
    • C. 2 + 2 + 2 + ...
    • D. 5 - 10 + 20 - ...
  3. 3. Write the repeating decimal $0.\overline{4}$ as a fraction in simplest form. The fraction is ___.

  4. 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. 5. An infinite geometric series diverges and does not have a sum if the absolute value of its common ratio $r$ is...

    • A. less than 1
    • B. greater than or equal to 1
    • C. equal to 0
    • D. a negative number
  6. 6. Use an infinite geometric series to convert the repeating decimal $0.\overline{8}$ to a fraction in simplest form. The fraction is ___.

  7. 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 $r$?

    • A. 0.1
    • B. 0.01
    • C. 0.001
    • D. 0.789
  8. 8. Convert the repeating decimal $0.\overline{12}$ into a fraction. Your answer should be in simplest form: ___.

  9. 9. Convert the repeating decimal $0.2\overline{3}$ into a fraction in simplest form. The result is ___.

  10. 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, $0.0\overline{1}$?

    • A. 0.4
    • B. 0.1
    • C. 0.01
    • D. 0.04