Question Number 33591 by abdo imad last updated on 19/Apr/18 $${find}\:{the}\:{value}\:{of}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\:\frac{\mathrm{2}}{{n}^{\mathrm{3}} \:\:+\mathrm{3}{n}^{\mathrm{2}} \:+\mathrm{2}{n}}\:. \\ $$ Commented by abdo imad last updated on 20/Apr/18…
Question Number 33592 by abdo imad last updated on 19/Apr/18 $${let}\:{f}\left({x}\right)\:={e}^{−{x}^{\mathrm{2}} } \\ $$$$\left.\mathrm{1}\right)\:{prove}\:{that}\:{f}^{\left({n}\right)} \left({x}\right)\:=\:{p}_{{n}} \left({x}\right).{e}^{−{x}^{\mathrm{2}} } \:\:\:{where}\:{p}_{{n}} {is}\:{a}\:{polynome} \\ $$$${with}\:{deg}={n} \\ $$$$\left.\mathrm{2}\right)\:{prove}\:{that}\:\forall\:{n}\geqslant\mathrm{1}\: \\ $$$${p}_{{n}+\mathrm{1}}…
Question Number 33588 by abdo imad last updated on 19/Apr/18 $${find}\:{the}\:{value}\:{of}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)\left(\mathrm{2}{n}+\mathrm{1}\right)}\:. \\ $$ Commented by abdo imad last updated on 20/Apr/18 $${let}\:{put}\:{S}_{{n}}…
Question Number 33586 by abdo imad last updated on 19/Apr/18 $${find}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:{z}^{{n}} \:\:\frac{{sin}\left({n}\theta\right)}{{n}}\:\:{with}\:{z}\:{from}\:{C}\:{and}\:\mid{z}\mid<\mathrm{1}\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 33584 by abdo imad last updated on 19/Apr/18 $${find}\:{the}\:{value}\:{of}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\left(\mathrm{1}+{i}\right)^{{n}} \:{cos}\left({n}\theta\right)}{\mathrm{2}^{{n}} }\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 33585 by abdo imad last updated on 19/Apr/18 $${study}\:{the}\:{nature}\:{of}\:\sum_{{n}=\mathrm{1}} ^{\infty} {sin}\left(\pi{en}!\right)\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 33583 by abdo imad last updated on 19/Apr/18 $${let}\:{z}\in{C}\:\:/\:\mid{z}\mid<\mathrm{1}\:\:{calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:{z}^{{n}} {cos}\left({n}\theta\right) \\ $$$${and}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:{z}^{{n}} \:{sin}\left({n}\theta\right) \\ $$ Terms of Service Privacy…
Question Number 33581 by abdo imad last updated on 19/Apr/18 $${find}\:{the}\:{nature}\:{of}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \left(−\mathrm{1}\right)^{{n}} \left(−\frac{\mathrm{1}}{{n}}\:+{arctan}\left(\frac{\mathrm{1}}{{n}}\right)\right)^{\frac{\mathrm{1}}{\mathrm{3}}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 33582 by abdo imad last updated on 19/Apr/18 $${find}\:{the}\:{nature}\:{of}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{{n}^{{ln}\left({n}\right)} }{{e}^{\sqrt{{n}}} }\:\:. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 99113 by mathmax by abdo last updated on 18/Jun/20 $$\mathrm{solve}\:\mathrm{y}^{''} \:+\mathrm{5y}^{'} \:−\mathrm{3y}\:=\mathrm{x}^{\mathrm{2}} \:\mathrm{sin}\left(\mathrm{3x}\right)\:\:\mathrm{with}\:\mathrm{y}\left(\mathrm{0}\right)\:=\mathrm{0}\:\mathrm{and}\:\mathrm{y}^{'} \left(\mathrm{0}\right)=−\mathrm{1} \\ $$ Answered by mathmax by abdo last updated…