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1-9-1-4-4-17-1-5-4-8-4-25-1-5-9-4-8-12-4-pi-2-2-2-3-4-




Question Number 122317 by Dwaipayan Shikari last updated on 15/Nov/20
1+9((1/4))^4 +17(((1.5)/(4.8)))^4 +25(((1.5.9)/(4.8.12)))^4 +...=(π/(2(√2)(Γ^2 ((3/4)))))
$$\mathrm{1}+\mathrm{9}\left(\frac{\mathrm{1}}{\mathrm{4}}\right)^{\mathrm{4}} +\mathrm{17}\left(\frac{\mathrm{1}.\mathrm{5}}{\mathrm{4}.\mathrm{8}}\right)^{\mathrm{4}} +\mathrm{25}\left(\frac{\mathrm{1}.\mathrm{5}.\mathrm{9}}{\mathrm{4}.\mathrm{8}.\mathrm{12}}\right)^{\mathrm{4}} +…=\frac{\pi}{\mathrm{2}\sqrt{\mathrm{2}}\left(\Gamma^{\mathrm{2}} \left(\frac{\mathrm{3}}{\mathrm{4}}\right)\right)} \\ $$

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