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lim-x-1-2-x-x-

Question Number 66019 by Rio Michael last updated on 07/Aug/19 $$\underset{{x}\rightarrow\infty} {{lim}}\:\left(\mathrm{1}\:+\:\frac{\mathrm{2}}{{x}}\right)^{{x}} \:= \\ $$ Commented by mathmax by abdo last updated on 07/Aug/19 $${let}\:{f}\left({x}\right)=\left(\mathrm{1}+\frac{\mathrm{2}}{{x}}\right)^{{x}}…

proof-or-given-a-counter-example-if-x-n-is-a-no-limited-sequence-then-exist-a-sub-sequence-x-nk-that-lim-n-0-1-x-nk-0-

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…

show-that-the-equation-xe-x-1-has-a-root-between-0-5-and-0-6-starting-with-0-55-as-a-first-approximate-

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

given-a-n-and-b-n-two-real-sequence-can-a-serie-n-1-a-n-and-n-1-b-n-diverge-but-n-1-a-n-b-n-converge-

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}…

f-actor-the-expression-completely-3-4-a-9-20-

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…

Simplify-1-2i-2-7-1-2i-7-

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}?…

a-n-1-a-n-1-cos-pin-2-a-n-1-n-sin-pin-2-a-0-0-a-1-1-a-10-

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…