### 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.