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Question Number 130092 by Adel last updated on 22/Jan/21

Commented by 0731619177 last updated on 24/Jan/21

$$hhhh$$

Answered by Dwaipayan Shikari last updated on 22/Jan/21

$$log{(-{(\frac{2}{\sqrt{2}}.\frac{2}{\sqrt{2+\sqrt{2}}}.\frac{2}{\sqrt{2+\sqrt{2+\sqrt{2}}}}...)}^3)}^1$$$$cos\frac{x}{2}cos\frac{x}{4}cos\frac{x}{8}...=\frac{sinx}{x}(x=\frac{\pi }{2})$$$$\Rightarrow \frac{\sqrt{2}}{2}.\frac{\sqrt{2+\sqrt{2}}}{2}.\frac{\sqrt{2+\sqrt{2+\sqrt{2}}}}{2}...=\frac{2}{\pi }$$$$=log\left({(-\frac{\pi }{2})}^3\right)=i\pi +3log\left(\frac{\pi }{2}\right)$$

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