Category: Relation and Functions

Question Number 46744 by math khazana by abdo last updated on 31/Oct/18 $${calculate}\:{S}_{{n}} =\sum_{\mathrm{0}\leqslant{i},{j}\leqslant{n}} \:\frac{{i}+{j}}{\mathrm{2}^{{i}+{j}} } \\ $$ Commented by MJS last updated on 31/Oct/18…

Question Number 112248 by 675480065 last updated on 06/Sep/20 $$\int_{−\frac{\pi\:\:\:}{\mathrm{2}}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{cos}^{\mathrm{2019}} \left(\mathrm{x}\right)\mathrm{cos}\left(\mathrm{2020x}\right)\mathrm{dx} \\ $$$$\mathrm{pls}\:\mathrm{help} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 46705 by math khazana by abdo last updated on 30/Oct/18 $${calculate}\:\sum_{{k}=\mathrm{0}} ^{{n}} \:\frac{\mathrm{1}}{\mathrm{3}{k}+\mathrm{1}}\:{interms}\:{of}\:{H}_{{n}} \\ $$$${H}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\mathrm{1}}{{k}}\:. \\ $$ Terms of Service…

Question Number 46610 by maxmathsup by imad last updated on 29/Oct/18 $${let}\:{f}_{{n}} \left({x}\right)={e}^{−{nx}} −\mathrm{2}{e}^{−\mathrm{2}{nx}} \:\:{with}\:{x}\:{from}\left[\mathrm{0},+\infty\left[\right.\right. \\ $$$$\left.\mathrm{1}\right){calculate}\:\int_{\mathrm{0}} ^{\infty} \:{f}_{{n}} \left({x}\right){dx}\:\:{and}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\left(\int_{\mathrm{0}} ^{\infty} \:{f}_{{n}} \left({x}\right){dx}\right)…

Question Number 46598 by maxmathsup by imad last updated on 29/Oct/18 $${calculate}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:{arctan}\left(\frac{\mathrm{1}}{{n}^{\mathrm{2}} \:+{n}+\mathrm{1}}\right) \\ $$ Commented by math khazana by abdo last updated…