Lesson 24 of 48
Series and convergence
Infinitely many terms that add to a finite number — sometimes.
Whether a sum settles or runs away is the same question as whether a training process converges. And the harmonic series is a permanent lesson in how slowly “diverges” can look like “settles.”
Do this
Show a geometric series with ratio below one converges and give its sum. Then sum the harmonic series in code out to a very large number of terms and watch it keep creeping up.
The question that unlocks the next lesson
The harmonic series 1 + 1/2 + 1/3 + 1/4 + … does what?
- AConverges to about 2.7
- BDiverges — it grows without bound, just very slowly
- CConverges to exactly 2
- DOscillates forever between two values