Is this series diverging? If not, what's the sum? – math.stackexchange.com

Is this series diverging? If not, what's the sum? – math.stackexchange.com

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The series in question: $$\frac{5}{7^2+11^2} + \frac{9}{11^2+15^2} + \frac{13}{15^2+19^2} + \dots$$ Or in a concise form: $$\sum_{i=1}^\infty {\frac{4i+1}{(4i+3)^2+(4i+7)^2}}$$ I tried to solve, ...

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