Topic 6 of 6
Sequences & Series
Decide convergence, work with power series, and understand what finite approximations can guarantee.
01Calculus · Direct answerWhy does the harmonic series diverge?Its terms approach zero, but they do so too slowly for the accumulated sum to settle.02Calculus · Concept explainerGeometric series: convergence, sum, and structureA constant ratio makes an infinite sum exactly solvable when repeated scaling shrinks toward zero.03Calculus · Decision guideHow to choose a convergence testMatch the series’ structure to a test instead of cycling through tests in chapter order.04Calculus · Method guideFinding a power series interval of convergenceFind the radius with the Ratio or Root Test, then test both endpoints separately because the general test goes silent there.05Calculus · Concept explainerTaylor remainder: how accurate is the polynomial?A Taylor polynomial is useful only with a way to control what was left out.