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give-z-cos-2pi-2015-isin-2pi-2015-find-S-1-z-z-2-z-3-z-2014-

Question Number 167916 by bounhome last updated on 29/Mar/22 $${give}:\:{z}={cos}\left(\frac{\mathrm{2}\pi}{\mathrm{2015}}\right)+{isin}\left(\frac{\mathrm{2}\pi}{\mathrm{2015}}\right) \\ $$$${find}\:{S}=\mathrm{1}+{z}+{z}^{\mathrm{2}} +{z}^{\mathrm{3}} +…+{z}^{\mathrm{2014}} \\ $$ Commented by benhamimed last updated on 29/Mar/22 $${z}={e}^{{i}\frac{\mathrm{2}\pi}{\mathrm{2015}}} \\…

If-a-2-b-2-1-then-1-b-ia-1-b-ia-

Question Number 167911 by MathsFan last updated on 29/Mar/22 $${If}\:\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} =\mathrm{1} \\ $$$$\:{then},\:\:\frac{\mathrm{1}+{b}+{ia}}{\mathrm{1}+{b}−{ia}}=? \\ $$ Answered by MJS_new last updated on 29/Mar/22 $$\frac{{b}+\mathrm{1}+{a}\mathrm{i}}{{b}+\mathrm{1}−{a}\mathrm{i}}=\frac{\left({b}+\mathrm{1}+{a}\mathrm{i}\right)^{\mathrm{2}} }{\left({b}+\mathrm{1}−{a}\mathrm{i}\right)\left({b}+\mathrm{1}+{a}\mathrm{i}\right)}=…

gt-2sin-5pi-12-sin-pi-12-slove-this-

Question Number 36821 by Ajayraj1995 last updated on 06/Jun/18 $$>.\:\mathrm{2}{sin}\frac{\mathrm{5}\pi}{\mathrm{12}}{sin}\frac{\pi}{\mathrm{12}}\:{slove}\:{this}.? \\ $$ Commented by maxmathsup by imad last updated on 06/Jun/18 $$=\mathrm{2}\:{sin}\left(\frac{\pi}{\mathrm{2}}\:−\frac{\pi}{\mathrm{12}}\right){sin}\left(\frac{\pi}{\mathrm{12}}\right)\:=\mathrm{2}{cos}\left(\frac{\pi}{\mathrm{12}}\right){sin}\left(\frac{\pi}{\mathrm{12}}\right)={sin}\left(\frac{\pi}{\mathrm{6}}\right)\:=\frac{\mathrm{1}}{\mathrm{2}}. \\ $$ Answered…

Question-102348

Question Number 102348 by mohammad17 last updated on 08/Jul/20 Answered by mr W last updated on 08/Jul/20 $${a}_{{n}} =\frac{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}} +\mathrm{1}}{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}} −\mathrm{1}} \\ $$$$=\mathrm{1}+\frac{\mathrm{2}}{\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}} −\mathrm{1}} \\…

Question-102347

Question Number 102347 by mohammad17 last updated on 08/Jul/20 Commented by bobhans last updated on 08/Jul/20 $$\mathrm{ln}\left(\mathrm{y}\right)\:=\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{1}}{{n}}\left(\mathrm{1}+\mathrm{cos}\:\left(\frac{{n}\pi}{\mathrm{2}}\right)\right) \\ $$$$\mathrm{ln}\left(\mathrm{y}\right)\:=\:\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}+\mathrm{cos}\:\left(\frac{{n}\pi}{\mathrm{2}}\right)}{{n}}\:=\:\mathrm{0} \\ $$$${y}\:=\:{e}^{\mathrm{0}} \:=\:\mathrm{1} \\…

A-particular-A-P-has-a-positive-common-difference-and-is-such-that-for-any-three-adjacent-terms-three-times-the-sum-of-their-squares-exceed-the-square-of-their-sum-by-37-5-Find-the-common

Question Number 167851 by otchereabdullai@gmail.com last updated on 27/Mar/22 $$\:\:\mathrm{A}\:\mathrm{particular}\:\mathrm{A}.\mathrm{P}\:\mathrm{has}\:\mathrm{a}\:\mathrm{positive}\: \\ $$$$\:\:\mathrm{common}\:\mathrm{difference}\:\mathrm{and}\:\mathrm{is}\:\mathrm{such}\:\mathrm{that} \\ $$$$\:\:\mathrm{for}\:\mathrm{any}\:\mathrm{three}\:\mathrm{adjacent}\:\mathrm{terms},\:\mathrm{three} \\ $$$$\:\mathrm{times}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{their}\:\mathrm{squares}\:\mathrm{exceed} \\ $$$$\:\mathrm{the}\:\mathrm{square}\:\mathrm{of}\:\mathrm{their}\:\mathrm{sum}\:\mathrm{by}\:\mathrm{37}.\mathrm{5}\:.\:\mathrm{Find} \\ $$$$\:\mathrm{the}\:\mathrm{common}\:\mathrm{difference}.\: \\ $$ Answered by mr…