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Home > CALC > Chapter 9 > Lesson 9.4.1 > Problem 9-114

9-114.
  1. Consider the infinite series below. For each, decide if it converges or diverges and justify your conclusion. If the series converges, find its sum. Homework Help ✎

    1. 0.9 + 0.99 + 0.999 + 0.9999 + ...

    2. 0.1 + 0.12 + 0.123 + 0.1234 + ...

    3. 256 − 128 + 64 − 32 + ...

For an infinite geometric series:

This is a geometric series with r = 1/2.

Think of this as:
0.9 + (0.9 + 0.09) + (0.9 + 0.09 + 0.009) + ...
What is happening to the value of each term?

See the hint in part (b).

This is a geometric series with r = –1/2.