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.
Example: Does the series converge?
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.