Warm Up Use summation notation to write the series for the specified number of terms. 5 + 7 + 9 + 11 + 13 + 15…; n = 7.

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Presentation transcript:

Warm Up Use summation notation to write the series for the specified number of terms. 5 + 7 + 9 + 11 + 13 + 15…; n = 7

Answer Use summation notation to write the series for the specified number of terms. 5 + 7 + 9 + 11 + 13 + 15…; n = 7

Convergent and Divergent Series

What will happen to the terms of this sequence as it continues forever? It approaches 0!

Convergent Sequence A sequence is converging if its terms approach 0. *Only applies to geometric sequences.

Determine if the following sequences are convergent or divergent:

Sum of an Infinite Geometric Series We can find the sum of this series, even though it goes on forever, because it is convergent.

Sum of an Infinite Geometric Series The following conditions must be true to use this formula: The series must be geometric The series must be convergent The series must be infinite

Example 1 Determine whether each infinite geometric series diverges or converges. If it converges, find the sum. a) 48 + 12 + 3 + … b) 4 + 8 + 16 + …

Example 2 Evaluate each infinite geometric series a) b)

Formula Recap Sequence Series Arithmetic Geometric Finite Infinite