Question Number 133829 by metamorfose last updated on 24/Feb/21 $${find}\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{x}^{{n}} {sin}\left({nx}\right)}{{n}}=…? \\ $$ Answered by Dwaipayan Shikari last updated on 24/Feb/21 $${log}\left(\mathrm{1}−{xe}^{{ix}} \right)={log}\left(\sqrt{\left(\mathrm{1}−{xcosx}\right)^{\mathrm{2}}…
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Question Number 2759 by RasheedAhmad last updated on 26/Nov/15 $${Without}\:{using}\:{arithmatic}\:{Series} \\ $$$${concept}\:{or}\:{formula}\:{prove}\:{the}\:{following}: \\ $$$$\mathrm{1}+\mathrm{2}+\mathrm{3}+…+{n}=\frac{{n}\left({n}+\mathrm{1}\right)}{\mathrm{2}} \\ $$ Answered by 123456 last updated on 26/Nov/15 $$\mathrm{induction} \\…
Question Number 133830 by metamorfose last updated on 24/Feb/21 $${find}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−{cos}\left({x}\right){cos}^{\mathrm{2}} \left(\mathrm{2}{x}\right){cos}^{\mathrm{3}} \left(\mathrm{3}{x}\right)…{cos}^{{n}} \left({nx}\right)}{{x}^{\mathrm{2}} }=…? \\ $$ Answered by EDWIN88 last updated on 24/Feb/21 $$\:\underset{{x}\rightarrow\mathrm{0}}…
Question Number 133825 by mnjuly1970 last updated on 24/Feb/21 Answered by mathDivergent last updated on 24/Feb/21 $$\frac{\mathrm{1}}{\mathrm{4}}\zeta\left(\mathrm{3}\right) \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 68289 by Rasheed.Sindhi last updated on 08/Sep/19 $$\mathrm{A}\:\mathrm{circle}\:\mathrm{is}\:\mathrm{divided}\:\mathrm{into}\:\mathrm{two}\:\mathrm{equal}\:\mathrm{parts} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{By} \\ $$$$\:\mathrm{An}\:\mathrm{arc}\:\mathrm{with}\:\mathrm{center}\:\mathrm{on}\:\mathrm{the}\:\mathrm{circle}. \\ $$$$\mathcal{D}{etermine} \\ $$$$\:\:\left({a}\right)\:{The}\:{length}\:{of}\:{the}\:{arc} \\ $$$$\:\:\left({b}\right){The}\:{ratio}\:{in}\:{which}\:{the}\:{arc} \\ $$$$\:\:\:\:\:\:\:\:{divides}\:{the}\:{diameter}\: \\ $$$$\:\:\:\:\:\:\:\:{meeting}\:{the}\:{center}\:{of}\:{the}\:{arc}. \\…
Question Number 133821 by bramlexs22 last updated on 24/Feb/21 $$\mathrm{There}\:\mathrm{are}\:\mathrm{5}\:\mathrm{positive}\:\mathrm{numbers}\: \\ $$$$\mathrm{and}\:\mathrm{6}\:\mathrm{negative}\:\mathrm{numbers}.\:\mathrm{Three}\: \\ $$$$\mathrm{numbers}\:\mathrm{are}\:\mathrm{chosen}\:\mathrm{at}\:\mathrm{random} \\ $$$$\mathrm{and}\:\mathrm{multiplied}\:.\:\mathrm{The}\:\mathrm{probability} \\ $$$$\mathrm{that}\:\mathrm{the}\:\mathrm{product}\:\mathrm{being}\:\mathrm{a}\:\mathrm{negative} \\ $$$$\mathrm{number}\:\mathrm{is}\: \\ $$$$\left(\mathrm{a}\right)\:\frac{\mathrm{17}}{\mathrm{33}}\:\:\:\left(\mathrm{b}\right)\:\frac{\mathrm{11}}{\mathrm{34}}\:\left(\mathrm{c}\right)\:\frac{\mathrm{16}}{\mathrm{33}}\:\:\:\left(\mathrm{d}\right)\:\frac{\mathrm{16}}{\mathrm{35}} \\ $$ Answered…
Question Number 2751 by prakash jain last updated on 26/Nov/15 $$\mathrm{Prove}\:\mathrm{that} \\ $$$$\underset{{i}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{sin}\:{i}}{{i}}=\frac{\pi}{\mathrm{2}}−\frac{\mathrm{1}}{\mathrm{2}} \\ $$ Answered by prakash jain last updated on 27/Nov/15…
Prove-that-i-2-n-gt-n-2-for-all-integral-values-of-n-5-ii-n-gt-3-n-1-for-all-integral-values-of-n-5-
Question Number 2750 by RasheedAhmad last updated on 26/Nov/15 $${Prove}\:{that}: \\ $$$$\left({i}\right)\:\:\mathrm{2}^{{n}} >{n}^{\mathrm{2}} \:\:{for}\:{all}\:{integral}\:{values} \\ $$$${of}\:\:{n}\geqslant\mathrm{5} \\ $$$$\left({ii}\right)\:{n}!>\mathrm{3}^{{n}−\mathrm{1}} ,{for}\:{all}\:{integral}\:{values} \\ $$$${of}\:{n}\geqslant\mathrm{5} \\ $$ Answered by…
Question Number 68285 by mezihloic last updated on 08/Sep/19 $${two}\:{students}\:{ngum}\:{ebon}\:{gave}\:{their}\:{ages}\:{as}\:\mathrm{124}_{\mathrm{4}} {and}\:\mathrm{33}_{{x}} {respectively}.{if}\:{both}\:{of}\:{them}\:{are}\:{of}\:{thesame}\:{ages}\:.{find}\:{in}\:{what}\:{base}\:{ebon}\:{gave}\:{her}\:{age} \\ $$ Commented by Rasheed.Sindhi last updated on 08/Sep/19 $$\mathrm{124}_{\mathrm{4}} ? \\ $$$$\mathrm{A}\:\mathrm{number}\:\mathrm{written}\:\mathrm{in}\:\mathrm{the}\:\mathrm{base}\:\mathrm{of}\:\mathrm{4}…