The Basel Problem — why 1 + 1/4 + 1/9 + ... = π²/6 #shorts #primenumbers #basel

Añadido: 2026-05-17

[00:00:00]1 + 1 + 1/9 + 1/16 forever. The sum of 1 over n squared, where does it go?

[00:00:08]It converges after 10 terms about 1.55.

[00:00:12]After 100, 1.63. After 1,000, 1.6439.

[00:00:17]It is homing in on something.

[00:00:20]Euler 1734 proved the answer.

[00:00:23]The sum equals pi squared over 6. Pi from a sum of reciprocal squares where there is no circle in sight.

[00:00:32]Why pi? Euler's trick. Factor sine of x as an infinite product with pi inside.

[00:00:38]Expand. Match coefficients. Pi falls out squared divided by 6.

[00:00:45]Pi squared over 6 approximately 1.6449.

[00:00:51]The Basel problem. Pi hiding inside a sum of squares.