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# The Direct Comparison Test (Note: all terms must be positive)

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1. The Direct Comparison Test (Note: all terms must be positive) Part 1 The seriesdiverges if there exists another seriessuch that bn < an and bn diverges, then the series diverges. Part 2 The seriesconverges if there exists another seriessuch that an <bn and bn converges, then the series converges.

2. Example: Does the series converge?

3. If , then both and converge or both diverge. Limit Comparison Test If and for all (N a positive integer) Note: To find an appropriate seies to compare with, consider leading terms of numerator and denominator of given series.

4. Example: Does the series converge?