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Euler’s Series: problem worth trying for RMO or INMO or Madhava Mathematics Competition

Mengoli posed the following series to be evaluated: $latex 1 + \frac{1}{2^{2}} + \frac{1}{3^{2}} + \frac{1}{4^{2}}+\ldots$ Some great mathematicians, including Leibnitz, John Bernoulli and D’…