Question Number 30552 by abdo imad last updated on 23/Feb/18 $${find}\:{s}\left({x}\right)=\:\sum_{{n}\geqslant\mathrm{0}} \:\frac{{sin}\left({na}\right)}{\left({sina}\right)^{{n}} }\:\frac{{x}^{{n}} }{{n}!}\:{and}\: \\ $$$${T}\left({x}\right)\:=\sum_{{n}\geqslant\mathrm{0}} \:\:\frac{{cos}\left({na}\right)}{\left({sina}\right)^{{n}} }\:\frac{{x}^{{n}} }{{n}!}\:. \\ $$ Terms of Service Privacy…
Question Number 30550 by abdo imad last updated on 23/Feb/18 $${let}\:{f}\left({z}\right)=\:\sum_{{n}\geqslant\mathrm{0}} {a}_{{n}} {z}^{{n}} \:\:\:/{a}_{\mathrm{0}} =\mathrm{1}\:,{a}_{\mathrm{1}} =\mathrm{3}\:{and}\:\forall{n}\geqslant\mathrm{2} \\ $$$${a}_{{n}} =\mathrm{3}{a}_{{n}−\mathrm{1}} −\mathrm{2}\:{a}_{{n}−\mathrm{2}} \:\:\:\:{find}\:{f}\left({z}\right)\:{for}\:\mid{z}\mid<\mathrm{1}\:\:\left({z}\in{C}\right)\:. \\ $$ Terms of…
Question Number 30549 by abdo imad last updated on 23/Feb/18 $${let}\:{S}\left({x}\right)=\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\frac{{x}^{\mathrm{3}{n}} }{\left(\mathrm{3}{n}\right)!}\:\:{find}\:{S}\left({x}\right). \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30547 by abdo imad last updated on 23/Feb/18 $${ind}\:{S}=\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\:\frac{{n}^{\mathrm{3}} \:+{n}^{\mathrm{2}} \:+{n}+\mathrm{1}}{{n}!}\:\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 30526 by abdo imad last updated on 22/Feb/18 $${let}\:{f}\left({x}\right)=\sqrt{\mathrm{1}+{ax}}\:\:{with}\:{a}\in{C}\:\:\:{find}\:\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right)\:{developp}\:{f}\left({x}\right)\:{at}\:{integr}\:{series}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
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…