### Home > CALC > Chapter 9 > Lesson 9.1.3 > Problem 9-45

9-45.

Determine whether each of the infinite series converges or diverges. Explain each answer briefly. If the series converges, find its exact sum.

What is

?

This is a geometric sequence with a ratio of

.

This is also a geometric sequence. What is the ratio? (See part (b).)

This can be written as a telescoping sum: