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Mathematics

Infinite Series

Quick fact

The geometric series 1/2 + 1/4 + 1/8 + 1/16 + ... converges to exactly 1, a fact used informally by ancient Greek philosopher Zeno in his paradoxes.

Why this is interesting

You can add 1 + 1/2 + 1/4 + 1/8 + ... forever and get a finite answer – but add 1 + 1/2 + 1/3 + 1/4 + ... forever and you'll reach infinity. Why does one infinite sum stop while another doesn't?