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sinh-1-1-2-sinh-1-2-2-sinh-1-3-2-




Question Number 123694 by Dwaipayan Shikari last updated on 27/Nov/20
sinh((1/1^2 ))+sinh((1/2^2 ))+sinh((1/3^2 ))+....
$${sinh}\left(\frac{\mathrm{1}}{\mathrm{1}^{\mathrm{2}} }\right)+{sinh}\left(\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }\right)+{sinh}\left(\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }\right)+…. \\ $$
Commented by Dwaipayan Shikari last updated on 27/Nov/20
Another approximation of sin((π/9))  sin((π/9))=(π/9)Π^∞ (1−(1/(81n^2 )))  sin((π/9))=(π/9)(1−(1/9^2 ))(1−(1/(18^2 )))(1−(1/(27^2 )))(1−(1/(36^2 )))(1−(1/(45^2 )))....
$${Another}\:{approximation}\:{of}\:{sin}\left(\frac{\pi}{\mathrm{9}}\right) \\ $$$${sin}\left(\frac{\pi}{\mathrm{9}}\right)=\frac{\pi}{\mathrm{9}}\overset{\infty} {\prod}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{81}{n}^{\mathrm{2}} }\right) \\ $$$${sin}\left(\frac{\pi}{\mathrm{9}}\right)=\frac{\pi}{\mathrm{9}}\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{9}^{\mathrm{2}} }\right)\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{18}^{\mathrm{2}} }\right)\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{27}^{\mathrm{2}} }\right)\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{36}^{\mathrm{2}} }\right)\left(\mathrm{1}−\frac{\mathrm{1}}{\mathrm{45}^{\mathrm{2}} }\right)…. \\ $$

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