4. Series of Numbers

4.3. Special Series

This is a brief listing of some of the most important series. Each of the convergence tests given in the previous section contains even more examples.

Geometric Series
converges absolutely for |a| < 1 to 1 / 1-a, diverges otherwise
p Series
converges for p > 1, diverges otherwise
Harmonic Series
Alternating Harmonic Series
converges conditionally
Euler's Series
converges to e (Euler's number)
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