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12.4 Convergent and Divergent Series

12.4 Convergent and Divergent Series. By the end of the period, students will be able to determine whether series is convergent or divergent as evidenced by a SmartBoard matching activity.

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12.4 Convergent and Divergent Series

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  1. 12.4 Convergent and Divergent Series By the end of the period, students will be able to determine whether series is convergent or divergent as evidenced by a SmartBoard matching activity.

  2. By the end of the period, students will be able to determine whether series is convergent or divergent as evidenced by a SmartBoard matching activity. Convergent Divergent The sequence of partial sums is infinite. • The sequence of partial sums approaches a limit Convergent vs. Divergent

  3. By the end of the period, students will be able to determine whether series is convergent or divergent as evidenced by a SmartBoard matching activity. • For the SUM to not change very much, we want very small (close to zero) values to continue to be added. • What types of series does this happen for? • Geometric ? • Terms get smaller and smaller..YES! • Geometric ? • Terms get bigger and bigger…NO!! • Arithmetic • Terms get bigger and bigger (either positive or negative)…NO! What do we want to happen?

  4. By the end of the period, students will be able to determine whether series is convergent or divergent as evidenced by a SmartBoard matching activity. • A series of the form • Where • This series CONVERGES!! P-series

  5. By the end of the period, students will be able to determine whether series is convergent or divergent as evidenced by a SmartBoard matching activity. • A series of the form • This series DIVERGES!! Since this is an arithmetic sequence that does not converge, anything LARGER than this sequence will also NOT CONVERGE. Harmonic Series

  6. By the end of the period, students will be able to determine whether series is convergent or divergent as evidenced by a SmartBoard matching activity. Summary of Series

  7. By the end of the period, students will be able to determine whether series is convergent or divergent as evidenced by a SmartBoard matching activity. • Complete the matching activity on the smart board software. Summary

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