Question Number 30519 by abdo imad last updated on 22/Feb/18 $${let}\:{j}={e}^{{i}\frac{\mathrm{2}\pi}{\mathrm{3}}} \:\:\:\:{find}\:{the}\:{value}\:{of}\:\sum_{{k}=\mathrm{0}} ^{{n}} {C}_{{n}} ^{{k}} \left(\mathrm{1}+{j}\right)^{{k}} {j}^{\mathrm{2}{n}−\mathrm{2}{k}} \:. \\ $$ Answered by sma3l2996 last updated…
Question Number 30509 by abdo imad last updated on 22/Feb/18 $${f}\:{function}\:{continue}\:{at}\:{o}\:{and}\:{lim}_{{x}\rightarrow\mathrm{0}} \frac{{f}\left(\mathrm{2}{x}\right)−{f}\left({x}\right)}{{x}}={l} \\ $$$${prove}\:{that}\:{f}\:{is}\:{derivable}\:{at}\:{o}\:{and}\:{f}^{'} \left(\mathrm{0}\right)={l}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30505 by abdo imad last updated on 22/Feb/18 $${find}\:\:{A}=\sum_{{k}=\mathrm{0}} ^{{n}} \:{ch}\left({a}+{kb}\right)\:{and}\:{B}=\sum_{{k}=\mathrm{0}} ^{{n}} \:{sh}\left({a}+{kb}\right). \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30495 by abdo imad last updated on 22/Feb/18 $${let}\:{f}\left({x}\right)=\sqrt{\mathrm{1}+{x}^{\mathrm{2}} \:}\:\:\:\:{find}\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:{calculate}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right). \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30496 by abdo imad last updated on 22/Feb/18 $${find}\:\:{A}_{{n}} =\:\sum_{{k}=\mathrm{0}} ^{{n}} \:{C}_{{n}} ^{{k}} \:{cos}\left({kx}\right)\:{and}\:{B}_{{n}} =\sum_{{k}=\mathrm{0}} ^{{n}} \:{C}_{{n}} ^{{k}} \:{sin}\left({kx}\right) \\ $$ Terms of…
Question Number 30492 by abdo imad last updated on 22/Feb/18 $${let}\:\left({u}_{\left.{n}\right)} \:\:\:/\:\:\:{u}_{{n}+\mathrm{1}} =\:{u}_{{n}} \:\:+\frac{\mathrm{1}}{{n}}\:\:\:{find}\:{a}\:{equivalent}\:{of}\:{u}_{{n}} \:{for}\right. \\ $$$${n}\rightarrow\infty\:. \\ $$$$ \\ $$ Terms of Service Privacy…
Question Number 30490 by abdo imad last updated on 22/Feb/18 $${f}\:{function}\:{derivable}\:{at}\:{o}\:{and}\:{f}\left(\mathrm{0}\right)=\mathrm{0}\:{let} \\ $$$${S}_{{n}} =\:\sum_{{k}=\mathrm{0}} ^{{n}} {f}\left(\frac{{k}}{{n}^{\mathrm{2}} }\right)\:\:.{find}\:{lim}_{{n}\rightarrow\infty} {S}_{{n}} . \\ $$ Terms of Service Privacy…
Question Number 30488 by abdo imad last updated on 22/Feb/18 $${let}\:\:\:{a}_{{n}} =\:\prod_{{k}=\mathrm{2}} ^{{n}} \:{cos}\left(\frac{\pi}{\mathrm{2}^{{k}} }\right)\:.{prove}\:{that}\:\left({a}_{{n}} \right)\:{ks}\:{decreasing}. \\ $$$$\left.\mathrm{2}\right)\:{let}\:{b}_{{n}} ={a}_{{n}} {cos}\left(\frac{\pi}{\mathrm{2}^{{n}} }\right)\:\:{find}\:{lim}_{{n}\rightarrow\infty} \left({a}_{{n}} \:−{b}_{{n}} \right). \\…
Question Number 30486 by abdo imad last updated on 22/Feb/18 $${let}\:{give}\:{a}_{{n}} =\:\prod_{{k}=\mathrm{1}} ^{{n}} \:{cos}\left(\:\frac{\pi}{\left({k}+\mathrm{2}\right)!}\right)\:{and} \\ $$$${b}_{{n}} =\prod_{{k}=\mathrm{1}} ^{{n}} \:\:{sin}\left(\frac{\pi}{\left({k}+\mathrm{2}\right)!}\right) \\ $$$$\left.\mathrm{1}\right)\:{find}\:{a}\:{equivalent}\:{foe}\:{a}_{{n}} \:{and}\:{b}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{a}\:{equivalent}\:{of}\:{a}_{{n}} .{b}_{{n}}…
Question Number 30485 by abdo imad last updated on 22/Feb/18 $$\left.\mathrm{1}\right)\:{prove}\:{that}\:\forall\:{x}>\mathrm{0}\:\:\:\frac{{x}}{{x}+\mathrm{1}}\:\leqslant\:{ln}\left(\mathrm{1}+{x}\right)\leqslant{x} \\ $$$$\left.\mathrm{2}\right)\:{let}\:{put}\:\:{S}_{{n}} =\:\prod_{{k}=\mathrm{1}} ^{{n}} \left(\mathrm{1}\:+\:\frac{{k}}{{n}}\right)\:{find}\:{lim}_{{n}\rightarrow\infty} \:{S}_{{n}} \:\:. \\ $$ Commented by chantriachheang last updated…