Question Number 3929 by Filup last updated on 25/Dec/15 $$\mathrm{For}: \\ $$$${S}=\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+…+\frac{\mathrm{1}}{{n}} \\ $$$${S}={H}_{{n}} \:\:\:\:{Harmonic}\:{sequence} \\ $$$${H}_{{n}} =\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{i}} \\ $$$${Can}\:{you}\:{solve}\:{the}\:{partial}\:{sum}? \\ $$ Commented…
Question Number 3928 by Filup last updated on 24/Dec/15 $$\mathrm{Is}\:\mathrm{this}\:\mathrm{solvable}: \\ $$$$ \\ $$$${y}=\lfloor{f}\left({x}\right)\rfloor\:\:\:\:\:\:\:\:\:\mathrm{floor}\:\mathrm{function} \\ $$$$\frac{{dy}}{{dx}}=??? \\ $$ Commented by Yozzii last updated on 25/Dec/15…
Question Number 69462 by mhmd last updated on 23/Sep/19 $$ \\ $$$${find}\:{the}\:{equation}\:{of}\:{the}\:{circle}\:{which}\:{ends}\:{one}\:{of}\:{the}\:{diameters}\:{of}\:{two}\:{points}\:{p}_{\mathrm{1}} \left(−\mathrm{2},\mathrm{3}\right)\:{and}\:{p}_{\mathrm{2}} \left(\mathrm{4},\mathrm{5}\right) \\ $$ Commented by mathmax by abdo last updated on 23/Sep/19…
Question Number 3927 by prakash jain last updated on 24/Dec/15 $$\mathrm{5}\:\mathrm{integers}\:\mathrm{are}\:\mathrm{selected}\:\mathrm{randomly}\:\mathrm{from}\:\mathbb{Z}^{+} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{at}\:\mathrm{least}\:\mathrm{one} \\ $$$$\mathrm{of}\:\mathrm{them}\:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{5}. \\ $$ Commented by prakash jain last updated on 26/Dec/15…
Question Number 69460 by mhmd last updated on 23/Sep/19 $${find}\:{the}\:{equation}\:{of}\:{the}\:{circle}\:{whose}\:{center}\:{is}\:{the}\:{origin}\:{and}\:{touches}\:{the}\:{line}\:\mathrm{3}{x}−\mathrm{4}{y}−\mathrm{15}=\mathrm{0} \\ $$ Commented by mathmax by abdo last updated on 23/Sep/19 $${equation}\:{of}\:{circle}\:{is}\:\:{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:={r}^{\mathrm{2}} \:\:{and}\:{r}\:={d}\left(\mathrm{0},{D}\right)…
Question Number 134998 by snipers237 last updated on 09/Mar/21 $$\:\:\:{Let}\:\:{I}=\:\int_{\mid{z}\mid=\pi} \frac{{tan}\left(\overset{−} {{z}}\right)}{{z}−\mathrm{4}}\:{dz}\:\: \\ $$$$\:{J}=\int_{\mid{z}\mid=\pi} \frac{{cos}\left(\overset{−} {{z}}\right)}{{z}−\mathrm{4}}\:{dz}\:\:\:{and}\:\:{K}=\int_{\mid{z}\mid=\pi} \frac{{cos}\left({Re}\left({z}\right)\right){cos}\left({Im}\left({z}\right)\right)}{{z}−\mathrm{4}}{dz} \\ $$$$\:{Show}\:{that}\:\:{I}={J}\sqrt{\mathrm{2}}=−{i}\pi \\ $$$$\:{Show}\:{that}\:\:{J}={K} \\ $$ Terms of…
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Question Number 69458 by mhmd last updated on 23/Sep/19 $${find}\:{the}\:{value}\:{sin}\left(−\mathrm{13}\pi/\mathrm{6}\right)\:,\:{cos}\left(\mathrm{49}\pi/\mathrm{4}\right) \\ $$$$ \\ $$ Commented by kaivan.ahmadi last updated on 23/Sep/19 $${sin}\left(−\mathrm{2}\pi−\frac{\pi}{\mathrm{6}}\right)={sin}\left(−\frac{\pi}{\mathrm{6}}\right)=−{sin}\left(\frac{\pi}{\mathrm{6}}\right)=−\frac{\mathrm{1}}{\mathrm{2}} \\ $$$${cos}\left(\frac{\mathrm{49}\pi}{\mathrm{4}}\right)={cos}\left(\mathrm{12}\pi+\frac{\pi}{\mathrm{4}}\right)={cos}\left(\frac{\pi}{\mathrm{4}}\right)=\frac{\sqrt{\mathrm{2}}}{\mathrm{2}} \\…
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Question Number 69456 by TawaTawa last updated on 23/Sep/19 Commented by TawaTawa last updated on 23/Sep/19 $$\mathrm{Help}\:\mathrm{with}\:\mathrm{number}\:\mathrm{5}\:\mathrm{too}\:\mathrm{sir}.\: \\ $$ Answered by mr W last updated…