Question Number 121362 by mnjuly1970 last updated on 07/Nov/20
$$\:\:\:\:\:\:\:...\:{advanced}\:\:{calculus}... \\ $$$$\:\:\:\:{evaluate}\:: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{K}=\underset{{n}\in\mathbb{N}} {\sum}\:\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{2}{n}} \left(\mathrm{1}+{cos}\left(\frac{\pi}{\mathrm{2}^{{n}} }\right)\right)}\:=? \\ $$
Commented by mindispower last updated on 07/Nov/20
$${have}\:{you}\:{the}\:{result}\:{not}\:{the}\:{answer} \\ $$
Answered by mindispower last updated on 07/Nov/20
$${i}\:{will}\:{try}\:{but}\:{not}\:{sur}\:,{tthis}\:\frac{\mathrm{1}}{\mathrm{1}+{cos}\left(\frac{\pi}{\mathrm{2}^{{n}} }\right)}\:{seems} \\ $$$${bee}\:{impressiv},{may}\:{bee}\:{turn}\:{it}\:{on}\:\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{1}+{tg}^{\mathrm{2}} \left(\frac{\pi}{\mathrm{2}^{{n}+\mathrm{1}} }\right)\right) \\ $$