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Big Ideas Math Algebra 2, 2014 View details

4. Finding Sums of Infinite Geometric Series

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Exercise 6 Page 439

To calculate the partial sum $S_{n},$ add the first $n$ terms.

Partial Sums: $S_{1} = 2,$ $S_{2} \approx 2.33,$ $S_{3} \approx 2.39,$ $S_{4} \approx 2.40,$ and $S_{5} \approx 2.40$
Graph:

Behavior: $S_{n}$ appears to approach $\frac{1 2}{5}$ or $2.4 .$

Practice makes perfect

Consider the given infinite geometric series.

2 + \frac{2}{6} + \frac{2}{3 6} + \frac{2}{2 1 6} + \frac{2}{1 2 9 6} + \dots

Let's start by finding the partial sums

S_{n}

for

n = 1,

2,

3,

4,

and

5 .

To calculate the partial sum

S_{n},

we need to add the first

n

terms.

$n$	Calculations	$S_{n}$
$1$	$-$	$2$
$2$	$2 + \frac{2}{6}$	$\frac{1 4}{6}$ $\approx$ $2.33$
$3$	$2 + \frac{2}{6} + \frac{2}{3 6}$	$\frac{8 6}{3 6}$ $\approx$ $2.39$
$4$	$2 + \frac{2}{6} + \frac{2}{3 6} + \frac{2}{2 1 6}$	$\frac{5 1 8}{2 1 6}$ $\approx$ $2.40$
$5$	$2 + \frac{2}{6} + \frac{2}{3 6} + \frac{2}{2 1 6} + \frac{2}{1 2 9 6}$	$\frac{3 1 1 0}{1 2 9 6}$ $\approx$ $2.40$

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Communicate Your Answer p.435

Monitoring Progress p.437-438

Exercise 6 Page 439

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