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Mathematics

The Curious Case of the Harmonic Series Divergence

Quick fact

If you could add one term every second, after 10^43 seconds (way longer than the age of the universe), the partial sum would still be less than 100.

Why this is interesting

You've probably learned that when you add smaller and smaller numbers, the sum settles down to a finite value. But what if the numbers shrink too slowly? Imagine adding 1 + 1/2 + 1/3 + 1/4 + ... forever—does this sum ever reach infinity?