the.com/convergent series
Infinite addition that gets bored and settles down to one number instead of running forever.
means A convergent series is an infinite sum of terms whose partial sums approach a single fixed number as you add more and more terms, rather than growing without bound or bouncing around forever.
from From Latin convergere — 'com-' (together) plus 'vergere' (to bend or incline) — the same root that gives us 'verge.' Mathematicians borrowed the word in the 17th-18th centuries to describe lines or quantities bending toward a common point. Applied to infinite series, it captures exactly that image: the running totals bend inward, homing in on one value instead of veering off to infinity. 'Series' itself comes from Latin 'series,' meaning a chain or row of linked things — fittingly, a row of terms strung together in sequence.
- test
- terms must shrink to zero, but that alone isn't enough
- classic trap
- 1/n diverges even though terms vanish
- famous case
- 1+1/2+1/4+... quietly equals 2
- real use
- makes calculus, physics, and your GPS math actually work