13-5

13-5 Sums of Infinite Series

-In this lesson, we learned how to find the sum of an infinite geometric series. Notice, I didn't include arithmetic; You can't find an infinite sum of an arithmetic series.

-Only geometric series where lrl < 1 have an infinite sum. Formula: S = t1/1-r

-In order to find were an infinite geometric converges, set lrl < 1, and solve for x.

-To write a repeating decimal as a fraction: what's repeating/place - 1

Example 1: Find the sum of the infinite geometric series 24 - 12 + 6 -3 +...

• S = t1/1 - r
• S = 24/1 - (-1/2)
• S = 24/1 + 1/2
• S = 16

Example 2: For the infinite geometric series, find the interval of convergence.

• 1 + x^2 + x^4 + x^6 +...
• lx^2l < 1
• -1 < x^2 < 1 (square root all three terms to get your answer)
• -1 < x < 1

Example 3: Express the given repeating decimal as a rational number; o.7777...

• 7/10-1 (the repeating decimal ends in the 10th's place)
• 7/9