Calculus 2B — Series & Taylor
When it does NOT converge
continues from lesson 1 — values defined earlier in the course stay live here
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 slowly. After 1000 terms it has crawled only to about 7.49.
= still climbing — it never stops
Real-world hook: the harmonic series is why a stack of identical books can overhang a table edge by any distance given enough books — the offsets add up like 1 + ½ + ⅓ + …