find-the-sum-1-x-1-2-x-2-1-4-x-4-1-2-n-x-2-n-1-

Question Number 197476 by universe last updated on 19/Sep/23

$$ \\ $$$$\:\:\:\mathrm{find}\:\mathrm{the}\:\mathrm{sum} \\ $$$$\:\frac{\mathrm{1}}{{x}+\mathrm{1}}+\frac{\mathrm{2}}{{x}^{\mathrm{2}} +\mathrm{1}}+\frac{\mathrm{4}}{{x}^{\mathrm{4}} +\mathrm{1}}+………+\frac{\mathrm{2}^{{n}} }{{x}^{\mathrm{2}^{{n}} } +\mathrm{1}}\:\:=\:?? \\ $$

Commented by witcher3 last updated on 19/Sep/23

sir You poste sum interesting Quation ∫_0 ^(π/2) ((ln(cos(x)))/(x^2 +1))dx...are You sur for the expression ?

$$\mathrm{sir}\:\mathrm{You}\:\mathrm{poste} \\ $$$$\mathrm{sum}\:\mathrm{interesting}\:\mathrm{Quation} \\ $$$$\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \frac{\mathrm{ln}\left(\mathrm{cos}\left(\mathrm{x}\right)\right)}{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\mathrm{dx}…\mathrm{are}\:\mathrm{You}\:\mathrm{sur}\:\mathrm{for}\:\mathrm{the}\:\mathrm{expression}\:? \\ $$

Commented by universe last updated on 20/Sep/23