Calculus 2B — Series & Taylor
Part 2 of 2. Geometric series that converge, the harmonic series that doesn't, and Taylor polynomials impersonating functions.
Part 2 of 2. Can you add infinitely many numbers and get a finite answer? Sometimes yes, sometimes no — and the difference powers everything from loan math to how your calculator computes sine.
- 01 Geometric series — infinite sums with finite answers ELI5: add 1 + ½ + ¼ + ⅛ + ⋯ forever and you do not get infinity — each term covers half the remaining gap to 2. Any geometric series (each term a fixed ratio r…
- 02 When it does NOT converge ELI5: shrinking terms are not enough. The harmonic series 1 + ½ + ⅓ + ¼ + ⋯ has terms heading to zero, yet its total grows without bound — just agonizingly…
- 03 Taylor series — polynomials impersonating functions ELI5: near a point, any smooth function can be mimicked by a polynomial built from its derivatives. The first two terms of sin(x) are x − x³/6; it hugs the…
next course: Linear Algebra A — Matrices & Determinants →