Alternating Series Test: Conditions, Error Bound, Examples
How the alternating series test works: the two conditions, the error bound, absolute vs conditional convergence, and worked examples with answers.
Tag: convergence
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Geometric Series Formula: Sum, Convergence and Examples
An infinite geometric series a + ar + ar² + … sums to a/(1 − r) when |r| < 1. Finite sum formula, derivation, repeating decimals and worked examples.
Ratio Test for Series Convergence: How to Use It (Examples)
The ratio test: if lim |aₙ₊₁/aₙ| 1 it diverges, = 1 inconclusive. Worked examples with factorials, powers and radius of convergence.
Improper Integrals: How to Tell If They Converge or Diverge
Improper integrals have infinite limits or infinite integrands. Learn the limit definition, the p-integral test, comparison, and 6 worked examples.