Strategy for Series
Consider a series in the form
- If
is apparent, then divergence test can be used. Otherwise look out for another way. - If
consists of a constant raised to a power of , geometric series can be used. - If
consists of raised to a constant power, p-series can be used. - If
consists of , alternating series test can be used. - If
consists of raised to a power of , root test would be suitable. - If
includes , ratio test must be used. - If
is a fraction, and consists of in both the denominator and the numerator, then direct comparison test or limit comparison test can be used. Consider the dominating parts to choose the . - If
is a positive and decreasing function, and is easy to evaluate, then integral test can be used.
Secret note on inequalities
For any
These inequalities can be used to find corresponding