18-20. Evaluating geometric series two ways Evaluate each geomet- ric series two ways. a. Find the nth partial sum S, of the series and evaluate lim S b. Evaluate the series using Theorem 10.7. k=0 THEOREM 10.7 Geometric Series a Let a + 0 and r be real numbers. If |r| < 1, then ark If |r| > 1, k=0 then the series diverges. Diverges rs-1 Converges -1

Algebra and Trigonometry (MindTap Course List)
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Chapter13: Sequences And Series
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18-20. Evaluating geometric series two ways Evaluate each geomet-
ric series two ways.
a. Find the nth partial sum S, of the series and evaluate lim S
b. Evaluate the series using Theorem 10.7.
k=0
Transcribed Image Text:18-20. Evaluating geometric series two ways Evaluate each geomet- ric series two ways. a. Find the nth partial sum S, of the series and evaluate lim S b. Evaluate the series using Theorem 10.7. k=0
THEOREM 10.7 Geometric Series
a
Let a + 0 and r be real numbers. If |r| < 1, then ark
If |r| > 1,
k=0
then the series diverges.
Diverges
rs-1
Converges
-1<r<1
Diverges
Transcribed Image Text:THEOREM 10.7 Geometric Series a Let a + 0 and r be real numbers. If |r| < 1, then ark If |r| > 1, k=0 then the series diverges. Diverges rs-1 Converges -1<r<1 Diverges
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