Sequences and series

Series convergence test practice problems L = \lim_{n\to\infty}\left|\frac{a_{n+1}}{a_n}\right|: \quad L < 1 \text{ converges},\ L > 1 \text{ diverges} 12 series convergence practice problems with answers: nth term, p-series, geometric, comparison, integral, ratio, root and alternating series tests. Power series practice problems \frac{1}{1 - x} = \sum_{n=0}^{\infty}x^n, \quad |x| < 1 12 power series practice problems with answers: radius and interval of convergence, endpoint checks, and building series from 1/(1 − x). Taylor series practice problems f(x) = \sum_{n=0}^{\infty}\frac{f^{(n)}(a)}{n!}(x - a)^n 12 Taylor and Maclaurin series practice problems with answers: building series, Taylor polynomials, estimates with error bounds, limits and sums. Parametric and polar practice problems \frac{dy}{dx} = \frac{dy/dt}{dx/dt}, \qquad A = \frac{1}{2}\int_{\alpha}^{\beta} r^2\,d\theta 12 parametric and polar practice problems with answers: dy/dx, tangent lines, arc length, converting coordinates, polar slopes and polar area.