The infinite series of 1/n^2, i.e 1+1/2^2+1/3^2+..., actually converges to a special number, namely, pi^2/6. This is a very famous math problem known as the Basel Problem and it does have many different solutions. I want to thank my viewer, Zvi H., for providing a spectacular solution to find the sum of 1/n^2 via a complex integral.
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