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13.5: Sums of Infinite Series

13.5: Sums of Infinite Series. Pre-Calculus. Warming Up. Find the sum of the first 5 terms: What do you think will happen to the sum???. Learning the Lingo/ Rules. Converge : To approach a limit Diverge : To fail to approach a limit

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13.5: Sums of Infinite Series

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  1. 13.5: Sums of Infinite Series Pre-Calculus

  2. Warming Up • Find the sum of the first 5 terms: • What do you think will happen to the sum???

  3. Learning the Lingo/ Rules • Converge: To approach a limit • Diverge: To fail to approach a limit • If , then the infinite geometric series converges to the sum . • If , then the series diverges.

  4. Example: Find the sum of the infinite geometric series: 9 – 6 + 4 – …

  5. Quick Practice! • Find the sum of the given infinite series, otherwise state that it diverges! 3/2 1/3 10/9

  6. Example: For what values of x does the following infinite geometric series converge? You broke my heart! Solution (1 < x < 3) is called the “interval of convergence”

  7. You Try… I dare you! -1 < x < 1

  8. Example: Convert the following into a rational number: 5/11

  9. Fastest Finisher gets prize(if correct; public humiliation otherwise!) .777 7/9

  10. Homework! • P.502: 1-8(odds), 14-18(evens), 24-28(evens)

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