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Warm UP!

Warm UP!. Solve: Express the series 2 + 6 + 10 + 14 + … + 54 Write out the terms of the series. Infinite Series Investigation With your elbow partner, please complete the front: number 1 and number 2 . You can divide the work however you want.

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Warm UP!

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  1. Warm UP! • Solve: • Express the series 2 + 6 + 10 + 14 + … + 54 • Write out the terms of the series

  2. Infinite Series Investigation With your elbow partner, please complete the front: number 1 and number 2. You can divide the work however you want. We will talk about the front and the back, and then we will take notes.

  3. Infinite Series Investigation 1) Consider the series: 1 + ½ + ¼ + … Make a table of the first 10 sums of this series (USE A CALCULATOR!). What do you notice happens to the sums? 2) Consider a similar series: 1 + 2 + 4 + …. Again, make a table. How is this table similar or different from the one above? Why do think this is so?

  4. LG 1-4: Infinite Series • Of the two series, which would have a sum of “infinity?” This is called a divergent series. • There is a formula to find the limit of a series that is convergent: • Find, using the formula above, the sum of the convergent infinite geometric series.

  5. What about arithmetic series? • An arithmetic series will always be divergent. • It’s sum will be negative infinity OR positive infinity • Decide which arithmetic series below will diverge to negative infinity: • 3 + 9 + 15 + 21 + … + (6n – 3) • 3 – 3 – 9 – 15 + …+ (-6n + 9)

  6. State whether the geometric series converges. If it does, find the sum of the infinite series. • 100 + 90 + 81 + … • 25 + 20 + 16 + … • 40 + 50 + 62.5 + … • 200 – 140 + 98 - …

  7. Class Work (Practice) • On your homework sheet from last night, pick 5 more from the back. • On the front, do 1 from each section (for a total of 3 problems) **These are partial sums, not infinite sums!** • HOMEWORK: On the blog tonight Don’t forget: QUIZ TOMORROW!

  8. Ticket out the door 3. Write an infinite geometric series that will have a sum of 12. Don’t forget: QUIZ TOMORROW!

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