Mathematics
Harmonic Series
Quick fact
The harmonic series is the most famous example of a divergent infinite series.
Why this is interesting
Did you know that adding up fractions like 1 + 1/2 + 1/3 + 1/4... can actually go on forever?
Read the full explanation
Understanding Harmonic Series
Imagine starting with 1, then adding half, then a third, then a quarter, and so on. Even though these numbers get smaller and smaller, they never add up to a finite number—they just keep growing, no matter how far you go.
A deeper explanation
The harmonic series is the sum of reciprocals of positive integers: 1 + 1/2 + 1/3 + 1/4 + ... This series diverges because, even though each term gets smaller, the partial sums grow without bound. It's a classic example used to show that not all infinite series converge, and it plays an important role in understanding convergence tests in calculus.