### The Basel Problem / The value of zeta two / Wallis' Product (TANTON Mathematics)

In 1644, Italian mathematician Mengoli asked for the exact value of the infinite sum of the reciprocals of the square numbers: 1 + 1/4 + 1/9 + 1/16 + 1/25 + ... = ?? He knew that the sum was bounded and wanted to know its value. Some ninety years later a young Leonhard Euler solved the problem and showed the exact answer to be (pi^2)/6. This is how Euler did it. (We'll also derive Wallis's product as a bonus!)

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07:50