Question Number 194868 by Erico last updated on 17/Jul/23 $$\mathrm{Prove}\:\mathrm{that}\:\forall{n}\in\mathrm{IN} \\ $$$$\underset{\:\mathrm{0}} {\int}^{\:\mathrm{1}} {t}\:{sin}^{\mathrm{2}{n}} \left({lnt}\right){dt}=\:\frac{\mathrm{1}}{\mathrm{1}−{e}^{−\mathrm{2}\pi} }\:\underset{\:\mathrm{0}} {\int}^{\:\pi} {e}^{−\mathrm{2}{t}} {sin}^{\mathrm{2}{n}} \left({t}\right){dt} \\ $$ Answered by witcher3…
Question Number 194781 by MM42 last updated on 15/Jul/23 $${f}_{{n}\:} \:\:{the}\:{general}\:{sentence}\:{is}\:{seqiencee} \\ $$$${fibonacci}.\: \\ $$$${prove}\:{that}\::\:\:{f}_{\mathrm{2}{n}−\mathrm{1}} ={f}_{{n}} ^{\mathrm{2}} +{f}_{{n}−\mathrm{1}} ^{\mathrm{2}} \\ $$$$ \\ $$ Terms of…
Question Number 194693 by MM42 last updated on 13/Jul/23 $${if}\:\:\:{f}_{{n}} ={f}_{{n}−\mathrm{1}} +{f}_{{n}−\mathrm{2}} \:\:;\:\:{f}_{\mathrm{1}} ={f}_{\mathrm{2}} =\mathrm{1} \\ $$$${then}\:\:\:{prove}\:{that}\:\:\:\mathrm{5}\mid{f}_{\mathrm{5}{n}} \:\: \\ $$ Answered by Frix last updated…
Question Number 194709 by MM42 last updated on 13/Jul/23 $${Show}\:{that}\:\:{in}\:{fibonacci}\:{sequence} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{f}_{\mathrm{3}{n}} ={f}_{{n}} ^{\mathrm{3}} +{f}_{{n}+\mathrm{1}} ^{\mathrm{3}} −{f}_{{n}−\mathrm{1}} ^{\mathrm{3}} \\ $$$$ \\ $$ Answered by TheHoneyCat…
Question Number 194446 by Spillover last updated on 07/Jul/23 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 64250 by Jameel Ahmad last updated on 16/Jul/19 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 129634 by abdurehime last updated on 17/Jan/21 $$\boldsymbol{{sin}}^{ } \boldsymbol{{x}}+\boldsymbol{{cos}}^{ } \boldsymbol{{x}}=\mathrm{1}\:\mathrm{proof}\:\mathrm{by}\:\mathrm{step}\:\mathrm{by}\:\mathrm{step}\:\mathrm{or}\:\mathrm{by}\:\mathrm{showing}\:\mathrm{all}\:\mathrm{steps}\: \\ $$$$\mathrm{b}/\mathrm{c}\:\mathrm{it}\:\mathrm{is}\:\mathrm{my}\:\mathrm{assignment} \\ $$ Answered by MJS_new last updated on 17/Jan/21…
Question Number 128246 by mnjuly1970 last updated on 05/Jan/21 $$\:\:\:\:\:\:\:\:\:\:\:\:\:\:…{nice}\:\:{calculus}… \\ $$$$\:\:{suppose}\:{that}\:\:::\:{m}=\frac{\mathrm{4}^{{p}} −\mathrm{1}}{\mathrm{3}}\:,\:\:{where} \\ $$$$\:\:\:\:\:\:\:{p}\:\:{is}\:\:{a}\:{prime}\:{number}\:{and}\:\:{p}>\mathrm{3}. \\ $$$${prove}\:\:{that}\:\:::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{2}^{{m}−\mathrm{1}} \:\overset{{m}} {\equiv}\:\mathrm{1}\:\:\:\:…? \\ $$$$\: \\ $$…
Question Number 127165 by sdfg last updated on 27/Dec/20 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 126808 by sdfg last updated on 24/Dec/20 Answered by JMZ last updated on 24/Dec/20 $${Since}\:\phi\:{is}\:{a}\:{homomorphism} \\ $$$$\phi\left({a}+{b}\right)=\phi\left({a}\right)+\phi\left({b}\right). \\ $$$${The}\:{kernel}\:{contais}\:{every}\:{x}\:{which} \\ $$ Answered by…