Question Number 6335 by FilupSmith last updated on 24/Jun/16 $$\mathrm{Can}\:\mathrm{you}\:\mathrm{show}\:\mathrm{me}\:\mathrm{why}: \\ $$$$\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}−\frac{\mathrm{1}}{\mathrm{4}}+…=\mathrm{ln}\left(\mathrm{2}\right) \\ $$$$\mathrm{or} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}+\mathrm{1}} }{{n}}=\mathrm{ln}\left(\mathrm{2}\right) \\ $$ Terms of Service Privacy…
Question Number 6334 by sanusihammed last updated on 24/Jun/16 Commented by nburiburu last updated on 24/Jun/16 $${basically}\:{you}\:\:{need}\:{to}\:{find}\:{first}\:{the}\:{common}\:{area}. \\ $$$${To}\:{do}\:{it},\:{let}\:{be}\:{M}\:{and}\:{N}\:{the}\:{intersection}\:{of}\:{both}\:{circles}\:{and}\:{O}\:{and}\:{P}\:\:{the}\:{centres}\:{of}\:{circle}\:{with}\:{radius}\:{b}\:{and}\:{a}\:,\:{respectively}. \\ $$$${the}\:{area}\:{couldbefound}\:{doing} \\ $$$${Area}.{circ}.{sector}\:\left({NOM}\right)\:+\:{Area}.{circ}.{sector}\:\left({MPO}\right)+{Area}.{circ}.{sector}\left({OPN}\right)\:−\:{Area}\bigtriangleup{MPO}\:−\:{Area}\bigtriangleup{OPN} \\ $$$${and}\:{for}\:{this}\:{is}\:{necessary}\:{to}\:{know}\:{two}\:\:{central}\:{angles}…
Question Number 71868 by naka3546 last updated on 21/Oct/19 Commented by prakash jain last updated on 21/Oct/19 $${f}\left({n}\right)=\mathrm{0} \\ $$ Commented by mr W last…
Question Number 6333 by FilupSmith last updated on 24/Jun/16 $${I}=\int_{\mathrm{0}} ^{\:{n}} \lfloor{x}\rfloor\lceil{x}\rceil{dx},\:\:{n}\in\mathbb{Z} \\ $$ Commented by nburiburu last updated on 24/Jun/16 $${I}=\underset{{i}=\mathrm{0}} {\overset{{n}} {\sum}}{i}\left({i}+\mathrm{1}\right) \\…
Question Number 137403 by BHOOPENDRA last updated on 02/Apr/21 Commented by BHOOPENDRA last updated on 02/Apr/21 $${please}\:{help}\:{me}\:{out}\:{this}\:{in}\:{correct}\:{way} \\ $$ Answered by liberty last updated on…
Question Number 71864 by Learner-123 last updated on 21/Oct/19 $${Draw}\:{the}\:{graph}\:{of}\:: \\ $$$${x}=\mid{y}\mid\:\sqrt{\mathrm{1}−{y}^{\mathrm{2}} } \\ $$ Commented by MJS last updated on 21/Oct/19 $$\mathrm{well},\:\mathrm{just}\:\mathrm{draw}\:\mathrm{it}? \\ $$$$\mathrm{table}…
Question Number 6329 by Rasheed Soomro last updated on 24/Jun/16 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{n}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following}\:\mathrm{series} \\ $$$$\frac{\mathrm{1}}{\mathrm{1}+\sqrt{\mathrm{x}}}+\frac{\mathrm{1}}{\mathrm{1}−\mathrm{x}}+\frac{\mathrm{1}}{\mathrm{1}−\sqrt{\mathrm{x}}}+…. \\ $$ Commented by FilupSmith last updated on 24/Jun/16 $${s}\mathrm{equence}\:{x},\:\sqrt{{x}},\:{x}…\:\mathrm{can}\:\mathrm{be}\:\mathrm{given}\:\mathrm{by}: \\ $$$$\frac{{x}}{\mathrm{2}}\left(\mathrm{1}−\left(−\mathrm{1}\right)^{{n}+\mathrm{1}}…
Question Number 6328 by Rasheed Soomro last updated on 24/Jun/16 $$\mathrm{Sum}\:\mathrm{0}.\mathrm{7}+\mathrm{0}.\mathrm{71}+\mathrm{0}.\mathrm{72}+….\mathrm{to}\:\mathrm{100}\:\mathrm{terms}. \\ $$ Commented by FilupSmith last updated on 24/Jun/16 $$\mathrm{difference}\:{d}\:=\:\mathrm{0}.\mathrm{01} \\ $$$$\mathrm{arithmetic}\:\mathrm{series}: \\ $$$$\therefore\:{S}=\frac{{n}}{\mathrm{2}}\left(\mathrm{2}{a}+\left({n}−\mathrm{1}\right){d}\right)…
Question Number 137397 by mnjuly1970 last updated on 02/Apr/21 $$\:…….\mathscr{A}{dvanced}\:…\:\:…\:\:…\:\mathscr{C}{alculus}……. \\ $$$$\:{simplify}\:::: \\ $$$$\:\Omega_{{n}} =\underset{{k}=\mathrm{1}} {\overset{\mathrm{2}{n}+\mathrm{1}} {\sum}}{log}\left(\mathrm{1}+{tan}\left(\frac{{k}\pi}{\mathrm{4}\left(\mathrm{2}{n}+\mathrm{1}\right)}\right)\right) \\ $$$$\:{moreover}\:,\:\:\:\:{find}\:{the}\:{value}\:{of}:: \\ $$$$\Omega=\:{lim}_{{n}\rightarrow\infty} \frac{\Omega_{{n}} }{{n}}\:=??? \\ $$…
Question Number 137398 by mohammad17 last updated on 02/Apr/21 Commented by mohammad17 last updated on 02/Apr/21 $${please}\:{sir}\:{help}\:{me} \\ $$ Terms of Service Privacy Policy Contact:…