Home > APCALC > Chapter 9 > Lesson 9.3.2 > Problem9-98

9-98.

Consider each of the infinite series below. For each series, decide if it converges or diverges and justify your conclusion. If the series converges, calculate its sum.

For an infinite geometric series:

$S=\frac{a}{1-r}\text{ }\Big|r\Big|<1$

1. $4 + 4 + 4 + 4 + …$

This is a geometric series with $r = 1$.

1. $\frac { 1 } { 10 } + \frac { 1 } { 100 } + \frac { 1 } { 1000 } + \ldots$

This is a geometric series with $r = 1/10$.

1. $10 + 9 + 8 + 7 + …$

This is an arithmetic series. Does an infinite arithmetic series have a finite sum?

1. $–2 +\frac { 6 } { 5 } - \frac { 18 } { 25 } + \frac { 54 } { 125 } - \ldots$

This is a geometric series with $r = -3/5$.