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- p-series
- convergent if p>1
- divergent if p≤1
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 or
- geometric series
- converges if |r|<1
- diverges if |r|≥1
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An is a rational function or algebraic function of n (involving roots of polynomials)
- comparison test with p-series
- the value of p should be chosen by keeping only the highest powers of n in the numerator and denomiator
- (i) Convergence: If Σbn is convergent, and an ≤ bn for all n, then Σan is convergent;
- (ii) Divergence: If Σbn is divergent, and an ≥ bn for all n, then Σan is divergent.
- NOTE: Comparison test only applies to series with positive terms. If it has negative terms, test for absol convergence.
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If series is similar to geo series
- comparison test with geo series
- NOTE: Comparison test only applies to series with positive terms. If it has negative terms, test for absol convergence.
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series with factorials, products (a constant raised to the nth power
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Harmonic series. Diverges
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If , where is easily evalutated
- Integral Test
- If if f is cts, positive and decreasing fcn on [1,∞), and an=f(n), then the series is convergent IFF is convergent
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If series is similar to p-series or geometric series
- Limit Comparison Test
- Given the series Σan, Σbn with positive terms,if , where c > 0 and finite, then the two series either both converge or both diverge.
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