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Question-134721

Question Number 134721 by 0731619177 last updated on 06/Mar/21 Commented by CutieJanab last updated on 06/Mar/21 $${i}\:{want}\:{to}\:{shre}\:{my}\:{queztion}\:{but}\:{i}\:{dont}\:{know}\:{how}\:{can}\:{i}\:{upload}\:{my}\:{wuestion}\:{cam}\:{you}\:{help}\:{me}… \\ $$ Commented by mr W last updated…

If-a-n-is-sum-of-the-all-primitive-n-th-root-of-unity-Does-n-1-a-n-converge-An-n-th-root-of-unity-say-z-is-primitive-if-it-is-not-k-th-root-of-unity-where-k-lt-n-or-z-n-1-and-z

Question Number 3650 by prakash jain last updated on 18/Dec/15 $$\mathrm{If}\:{a}_{{n}} \:\mathrm{is}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{all}\:\mathrm{primitive}\:{n}^{{th}} \:\mathrm{root}\:\mathrm{of} \\ $$$$\mathrm{unity}. \\ $$$$\mathrm{Does}\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}{a}_{{n}} \:\mathrm{converge}? \\ $$$$\mathrm{An}\:{n}^{{th}} \:\mathrm{root}\:\mathrm{of}\:\mathrm{unity},\:\mathrm{say}\:{z},\:\mathrm{is}\:\mathrm{primitive}\:\mathrm{if}\:\mathrm{it}\:\mathrm{is}\:\mathrm{not} \\ $$$${k}^{{th}}…

Draw-a-line-segment-equal-to-ab-units-when-AB-a-units-and-CD-b-units-are-given-Only-ruler-and-compass-may-be-used-

Question Number 3647 by Rasheed Soomro last updated on 17/Dec/15 $${Draw}\:{a}\:{line}\:{segment}\:{equal}\:{to} \\ $$$$\boldsymbol{{ab}}\:{units}\:{when}\:{AB}=\boldsymbol{{a}}\:{units}\:\:{and}\:{CD}=\boldsymbol{{b}}\:{units}\: \\ $$$${are}\:{given}.\:{Only}\:{ruler}\:{and}\:{compass}\:{may}\:{be} \\ $$$${used}. \\ $$ Commented by prakash jain last updated…

ln-x-x-1-dx-

Question Number 134716 by metamorfose last updated on 06/Mar/21 $$\int\frac{{ln}\left({x}\right)}{{x}−\mathrm{1}}{dx}=…?? \\ $$ Answered by Lordose last updated on 06/Mar/21 $$\int\frac{\mathrm{ln}\left(\mathrm{x}\right)}{\mathrm{x}−\mathrm{1}}\mathrm{dx}\:\overset{\mathrm{u}=\mathrm{x}−\mathrm{1}} {=}\int\frac{\mathrm{ln}\left(\mathrm{1}+\mathrm{u}\right)}{\mathrm{u}}\mathrm{du}\:=\:−\mathrm{Li}_{\mathrm{2}} \left(−\mathrm{u}\right)\:+\:\mathrm{C} \\ $$$$\Omega\:=\:−\mathrm{Li}_{\mathrm{2}} \left(\mathrm{1}−\mathrm{x}\right)\:+\:\mathrm{C}…

Question-134719

Question Number 134719 by 0731619177 last updated on 06/Mar/21 Commented by Dwaipayan Shikari last updated on 06/Mar/21 $$\pi^{\frac{\mathrm{3}}{\mathrm{2}}} −\frac{\mathrm{3}\pi}{\mathrm{2}}.\frac{\Gamma\left(\frac{\mathrm{5}}{\mathrm{3}}\right)}{\Gamma\left(\frac{\mathrm{7}}{\mathrm{6}}\right)} \\ $$ Answered by CutieJanab last…

An-hexagon-of-unit-side-is-drawn-on-plane-Draw-a-square-having-the-same-area-as-the-hexagon-using-only-unmarked-ruler-and-compass-What-if-an-n-gon-with-unit-edges-is-given-Is-it-always-possible-to

Question Number 3644 by prakash jain last updated on 17/Dec/15 $$\mathrm{An}\:\mathrm{hexagon}\:\mathrm{of}\:\mathrm{unit}\:\mathrm{side}\:\mathrm{is}\:\mathrm{drawn}\:\mathrm{on}\:\mathrm{plane}. \\ $$$$\mathrm{Draw}\:\mathrm{a}\:\mathrm{square}\:\mathrm{having}\:\mathrm{the}\:\mathrm{same}\:\mathrm{area}\:\mathrm{as}\:\mathrm{the} \\ $$$$\mathrm{hexagon}\:\mathrm{using}\:\mathrm{only}\:\mathrm{unmarked}\:\mathrm{ruler}\:\mathrm{and}\: \\ $$$$\mathrm{compass}. \\ $$$$\mathrm{What}\:\mathrm{if}\:\mathrm{an}\:{n}−\mathrm{gon}\:\mathrm{with}\:\mathrm{unit}\:\mathrm{edges}\:\mathrm{is}\:\mathrm{given}? \\ $$$$\mathrm{Is}\:\mathrm{it}\:\mathrm{always}\:\mathrm{possible}\:\mathrm{to}\:\mathrm{draw}\:\mathrm{a}\:\mathrm{square} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{same}\:\mathrm{area}\:\mathrm{as}\:{n}−\mathrm{gon}\:\mathrm{using}\:\mathrm{ruler} \\ $$$$\mathrm{and}\:\mathrm{compass}.…