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Today in Precalculus

Explore the concept of infinite series in precalculus. Learn how to determine if a series converges or diverges and calculate the sum of geometric and arithmetic sequences. Practice homework problems to reinforce your understanding.

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Today in Precalculus

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  1. Today in Precalculus • Go over homework • Notes: Infinite Series(no handout, need a calculator) • Homework

  2. Series Example: Find the sum of the geometric series: 8 + 4 + 2 + … + 1/32 What happens if we change n to a) 20, b) 50, c) 100?

  3. Infinite Series This expression is called an infinite series

  4. Infinite Series An infinite series can either: • Converge – if, as n increases, the series sum approaches a value (S) • Diverge – if as n increases, the series sum does NOT approach a value.

  5. Example Diverges Do the following series converge or diverge? • 2 + 4 + 6 + 8 + 10 +… • 1 + (-3) + 9 + (-27) + 216 + … Converges Diverges Can an infinite arithmetic series converge?

  6. Sum of an Infinite Geometric Series

  7. Does the following series converge? If so, give the sum. So it converges

  8. Do the following series converge? If so, give the sum. So it diverges So it converges

  9. Does the following series converge? If so, give the sum. So it converges

  10. Homework • Worksheet • Chapter 9 Test: January 26

  11. Series =16 At some point the calculator begins to round off (1 – 1/2n) to 1 =16

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