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Chapter 10Series

0110.01Series Notation and Indexing
0210.02Sequence of Partial Sums
0310.03Convergence/Divergence
0410.04The Harmonic Series
0510.05Geometric Series
0610.06Telescoping Series
0710.07Divergence Test
0810.08Integral Test and p-series
0910.09Comparison and Limit Comparison Tests
1010.10Alternating Series Test
1110.11Absolute and Conditional Convergence
1210.12Ratio and Root Test

Chapter 10 · Series

0110.01Series Notation and Indexing
0210.02Sequence of Partial Sums
0310.03Convergence/Divergence
0410.04The Harmonic Series
0510.05Geometric Series
0610.06Telescoping Series
0710.07Divergence Test
0810.08Integral Test and p-series
0910.09Comparison and Limit Comparison Tests
1010.10Alternating Series Test
1110.11Absolute and Conditional Convergence
1210.12Ratio and Root Test

Topics / 10 Series

10.12

Ratio and Root Test

Compare each term with the one before (ratio) or take n-th roots (root). Below 1 converges, above 1 diverges, exactly 1 tells you nothing.

About 16 minutes

You'll learn to

→Apply the ratio test
→Apply the root test
→Know when each test is the right tool
→Recognize the inconclusive case

← 10.11 Absolute and Conditional Convergence 11.01 Estimating the Value of a Series →

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