Strategy for Testing Series
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 pseries
 convergent if p>1
 divergent if p≤1

or
 geometric series
 converges if r<1
 diverges if r≥1

An is a rational function or algebraic function of n (involving roots of polynomials)
 comparison test with pseries
 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 a_{n} ≤ b_{n} for all n, then Σa_{n} is convergent;
 (ii) Divergence: If Σbn is divergent, and a_{n} ≥ b_{n} for all n, then Σa_{n} is divergent.
 NOTE: Comparison test only applies to series with positive terms. If it has negative terms, test for absol convergence.

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.



series with factorials, products (a constant raised to the nth power

Harmonic series. Diverges


If
, where
is easily evalutated
 Integral Test
 If if f is cts, positive and decreasing fcn on [1,∞), and a_{n}=f(n), then the series is convergent IFF is convergent

If series is similar to pseries or geometric series
 Limit Comparison Test
 Given the series Σa_{n}, Σb_{n} with positive terms,if , where c > 0 and finite, then the two series either both converge or both diverge.