Sum of double integrals

Calculus Level 4

\[ \large \sum_{n=1}^\infty \iint_{R} \left(\frac y{\sqrt{x^2+y^2}} \right)^n \, dx dy \]

Given that \(R= \{ (x,y) \in \mathbb R^2 : y \leq x, x^2 + y^2 \leq 2, y \geq 0 \} \).

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