Home > CALC > Chapter 9 > Lesson 9.4.1 > Problem 9-114
9-114.
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 ✎
0.9 + 0.99 + 0.999 + 0.9999 + ...
0.1 + 0.12 + 0.123 + 0.1234 + ...
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.