Question Number 481 by 123456 last updated on 12/Jan/15 $${proof}\:{or}\:{given}\:{a}\:{counter}\:{example}: \\ $$$${if}\:\left\{{x}_{{n}} \right\}\:{is}\:{a}\:{no}\:{limited}\:{sequence} \\ $$$${then} \\ $$$${exist}\:{a}\:{sub}−{sequence}\:\left\{{x}_{{nk}} \right\}\:{that} \\ $$$$\underset{{n}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{1}}{{x}_{{nk}} }=\mathrm{0} \\ $$ Commented…
Question Number 66017 by Rio Michael last updated on 07/Aug/19 $${show}\:{that}\:{the}\:{equation}\:{xe}^{{x}} =\mathrm{1}\:{has}\:{a}\:{root}\:{between}\:\mathrm{0}.\mathrm{5}\:{and}\:\mathrm{0}.\mathrm{6}\:{starting} \\ $$$${with}\:\mathrm{0}.\mathrm{55}\:{as}\:{a}\:{first}\:{approximate}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 476 by 123456 last updated on 11/Jan/15 $${given}\:{a}_{{n}} \:{and}\:{b}_{{n}} \:{two}\:{real}\:{sequence} \\ $$$${can}\:{a}\:{serie}\:\underset{{n}=\mathrm{1}} {\overset{+\infty} {\sum}}{a}_{{n}} \:{and}\:\underset{{n}=\mathrm{1}} {\overset{+\infty} {\sum}}{b}_{{n}} \:{diverge} \\ $$$${but} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{+\infty}…
Question Number 460 by Karting7442 last updated on 25/Jan/15 $${Factor}\:{completely}\:\:\mathrm{2}.\mathrm{4}{c}+\mathrm{6}\:\:\:{please}\:{help}\:{me} \\ $$ Answered by prakash jain last updated on 09/Jan/15 $$\mathrm{2}.\mathrm{4}{c}+\mathrm{6}=\mathrm{6}\left(\mathrm{0}.\mathrm{4}{c}+\mathrm{1}\right) \\ $$ Terms of…
Question Number 459 by Karting7442 last updated on 25/Jan/15 $$\underset{} {{f}actor}\:{the}\:{expression}\:{completely}:\:\frac{\mathrm{3}}{\mathrm{4}}{a}−\frac{\mathrm{9}}{\mathrm{20}} \\ $$ Answered by prakash jain last updated on 09/Jan/15 $$\frac{\mathrm{3}}{\mathrm{4}}{a}−\frac{\mathrm{9}}{\mathrm{20}}=\frac{\mathrm{3}}{\mathrm{4}}\left({a}−\frac{\mathrm{3}}{\mathrm{5}}\right) \\ $$ Terms…
Question Number 451 by Karting7442 last updated on 25/Jan/15 $${solve}\:{the}\:{equation}\:{for}\:{x}\:\::\:\mathrm{5}−{x}=\:−\mathrm{3} \\ $$ Answered by prakash jain last updated on 09/Jan/15 $$\mathrm{5}−{x}=−\mathrm{3} \\ $$$${x}=\mathrm{5}+\mathrm{3}=\mathrm{8} \\ $$…
Question Number 65983 by Rio Michael last updated on 07/Aug/19 $$\:{Simplify}\: \\ $$$$\:\:\:\left(\mathrm{1}+\:\mathrm{2}{i}\sqrt{\mathrm{2}}\right)^{\mathrm{7}} \:−\:\left(\mathrm{1}\:+\mathrm{2}{i}\right)^{\mathrm{7}} \\ $$ Commented by Rio Michael last updated on 17/Aug/19 $${can}\:{i}\:{use}\:{de}\:{moivre}'{s}\:{theorem}?…
Question Number 440 by 123456 last updated on 25/Jan/15 $${a}\left({n}+\mathrm{1}\right)=\left[{a}\left({n}\right)+\mathrm{1}\right]\mathrm{cos}\left(\frac{\pi{n}}{\mathrm{2}}\right)+\left[{a}\left({n}−\mathrm{1}\right)+{n}\right]\mathrm{sin}\:\left(\frac{\pi{n}}{\mathrm{2}}\right) \\ $$$${a}\left(\mathrm{0}\right)=\mathrm{0} \\ $$$${a}\left(\mathrm{1}\right)=\mathrm{1} \\ $$$${a}\left(\mathrm{10}\right)=? \\ $$ Answered by prakash jain last updated on…
Question Number 131507 by Chhing last updated on 05/Feb/21 $$ \\ $$$$\:\:\:\mathrm{1}/\mathrm{Show}\:\mathrm{that}\:\left(\mathrm{2019}\right)^{\mathrm{2021}} +\left(\mathrm{2021}\right)^{\mathrm{2019}} \:\mathrm{divided}\:\:\mathrm{by}\:\mathrm{2020} \\ $$$$\:\:\:\mathrm{2}/\mathrm{Show}\:\mathrm{that}\:\mathrm{2222}^{\mathrm{5555}} +\mathrm{5555}^{\mathrm{2222}} \:\mathrm{divided}\:\:\mathrm{by}\:\mathrm{7} \\ $$$$ \\ $$ Answered by JDamian…