[挑戰]級數hk

香港級數問題 

Let {x_n} be a sequence of positive real number, If x₁ = 3/2 and x_n+1² – x_n² = 1/(n+2)² – 1/n² for all positive integers n, find x₁ + x₂ + x₃ + … + x₂₀₀₈

(xn+1)^2 – xn^2 = 1/(n+2)^2 – 1/n^2 

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