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Question Number 175967 by infinityaction last updated on 10/Sep/22

 lim_(nโ†’โˆž)  [tan๐šฟ+(1/2)tan(๐šฟ/2)+(1/2^2 )tan(๐šฟ/2^2 )+...+(1/2^n )tan(๐šฟ/2^n )]

$$\:\underset{\boldsymbol{{n}}\rightarrow\infty} {\boldsymbol{\mathrm{lim}}}\:\left[\boldsymbol{\mathrm{tan}\Psi}+\frac{\mathrm{1}}{\mathrm{2}}\boldsymbol{\mathrm{tan}}\frac{\boldsymbol{\Psi}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}} }\boldsymbol{\mathrm{tan}}\frac{\boldsymbol{\Psi}}{\mathrm{2}^{\mathrm{2}} }+...+\frac{\mathrm{1}}{\mathrm{2}^{\boldsymbol{{n}}} }\boldsymbol{\mathrm{tan}}\frac{\boldsymbol{\Psi}}{\mathrm{2}^{\boldsymbol{{n}}} }\right]\:\:\:\:\: \\ $$

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