Arithmetic and Geometric Sequences: Formulas and Sums
Arithmetic and geometric sequence formulas for the nth term and the sum, sigma notation, infinite geometric series, and worked examples with answers.
Category: Series
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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.
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.
Taylor and Maclaurin Series: Formula and Examples
The Taylor series formula, how to build Taylor polynomials step by step, a table of common Maclaurin series (eˣ, sin x, cos x, ln(1+x)), and error bounds.