textbook-theory · English
The Sum of a Sequence
Section 1.3 of Dan Sloughter's open calculus textbook 'Difference Equations to Differential Equations' introduces the concept of infinite series as limits of partial sums. The section develops the theory of geometric series, derives the closed-form sum formula for |r| < 1, and demonstrates applications including probability problems (coin tossing, animal reproduction), the economic multiplier effect, and the divergence of the harmonic series.
infinite seriesgeometric seriesconvergenceharmonic series