Question Number 85832 by jagoll last updated on 25/Mar/20 $$\left(\mathrm{x}+\mathrm{x}^{−\mathrm{1}} \right)^{\mathrm{2}} +\left(\mathrm{x}^{\mathrm{2}} +\mathrm{x}^{−\mathrm{2}} \right)^{\mathrm{2}} +\left(\mathrm{x}^{\mathrm{3}} +\mathrm{x}^{−\mathrm{3}} \right)^{\mathrm{2}} \\ $$$$+\:…\:+\:\left(\mathrm{x}^{\mathrm{10}} +\mathrm{x}^{−\mathrm{10}} \right)^{\mathrm{2}} \:=\: \\ $$ Commented…
Question Number 20235 by naziri1920@gmail.com last updated on 24/Aug/17 $$ \\ $$$${if}\:\:\:\:\:\:\:\:{t}_{\left({m}+\mathrm{1}\right)} =\mathrm{2}{t}_{\left({n}+\mathrm{1}\right)} \\ $$$${so}\:{proof} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{t}_{\left(\mathrm{3}{m}+\mathrm{1}\right)} =\mathrm{2}{t}_{\left({m}+{n}+\mathrm{1}\right)\:\:\:\:\:\:} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{help}\:{please}……… \\ $$$$ \\ $$$$ \\…
Question Number 20217 by tawa tawa last updated on 24/Aug/17 Commented by tawa tawa last updated on 24/Aug/17 $$\mathrm{Please}\:\mathrm{help} \\ $$ Terms of Service Privacy…
Question Number 151256 by pticantor last updated on 19/Aug/21 $$\:{A}_{{n}} =\mathrm{2}^{{n}} +\mathrm{3}^{{n}} +\mathrm{4}^{{n}} +\mathrm{5}^{{n}} \\ $$$${B}_{{n}} =\mathrm{100}^{{n}} +\mathrm{101}^{{n}} +\mathrm{102}^{{n}} +\mathrm{103}^{{n}} \\ $$$$\left.\mathrm{1}\right)\boldsymbol{{find}}\:\boldsymbol{{values}}\:\boldsymbol{{of}}\:\boldsymbol{{n}}\:\boldsymbol{{while}}\:\mathrm{7}\mid\boldsymbol{{A}}_{\boldsymbol{{n}}} \\ $$$$\left.\mathrm{2}\right)\:\boldsymbol{{show}}\:\boldsymbol{{that}}\:\boldsymbol{{B}}_{\boldsymbol{{n}}} \equiv\boldsymbol{{A}}_{\boldsymbol{{n}}}…
Question Number 151216 by liberty last updated on 19/Aug/21 $$\:\:\:\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{number}\: \\ $$$$\:\:\sqrt[{\mathrm{7}}]{\mathrm{x}+\mathrm{3}}\:+\sqrt[{\mathrm{7}}]{\mathrm{6}−\mathrm{x}}\:=\:\sqrt[{\mathrm{7}}]{\mathrm{9}}\: \\ $$ Answered by MJS_new last updated on 19/Aug/21 $$\mathrm{very}\:\mathrm{obviously}\:{x}=−\mathrm{3}\vee{x}=\mathrm{6} \\ $$ Commented…
Question Number 85588 by TawaTawa1 last updated on 23/Mar/20 Commented by john santu last updated on 23/Mar/20 $$\mathrm{14},\mathrm{450}\:=\:\frac{{a}\left(\mathrm{4}^{{n}} −\mathrm{1}\right)}{\mathrm{3}} \\ $$$$\mathrm{43},\mathrm{350}\:=\:{a}\:\left(\mathrm{4}^{{n}} −\mathrm{1}\right) \\ $$$${a}\:=\:\frac{\mathrm{43},\mathrm{350}}{\mathrm{4}^{{n}} −\mathrm{1}}\:\Rightarrow\:\mathrm{100}<\frac{\mathrm{43},\mathrm{350}}{\mathrm{4}^{{n}}…
Question Number 85546 by TawaTawa1 last updated on 22/Mar/20 Commented by TawaTawa1 last updated on 23/Mar/20 $$\mathrm{Given}\:\mathrm{that}\:\mathrm{the}\:\mathrm{sum},\:\mathrm{S},\:\:\mathrm{of}\:\mathrm{a}\:\mathrm{geometric}\:\mathrm{series}\:\mathrm{with}\:\mathrm{a}\:\mathrm{common} \\ $$$$\mathrm{ratio}\:\:\mathrm{4}\:\:\mathrm{is}\:\:\mathrm{14},\mathrm{450}.\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the}\:\mathrm{starting}\:\mathrm{value} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{series}\:\mathrm{if}\:\mathrm{it}\:\mathrm{is}\:\mathrm{an}\:\mathrm{integer}\:\mathrm{and}\:\mathrm{lies}\:\mathrm{between}\:\mathrm{100}\:\mathrm{and}\:\mathrm{500}. \\ $$$$\mathrm{Does}\:\mathrm{your}\:\mathrm{answer}\:\mathrm{agree}\:\mathrm{with}\:\mathrm{output}\:\mathrm{of}\:\mathrm{the}\:\mathrm{formular}\:\mathrm{for}\:\mathrm{the} \\ $$$$\mathrm{sum}\:\mathrm{of}\:\mathrm{a}\:\mathrm{geometric}\:\mathrm{series}\:\left(\mathrm{given}\:\mathrm{below}\right)?.\:\mathrm{Show}\:\mathrm{your}\:\mathrm{workings}…
Question Number 151079 by mathdanisur last updated on 18/Aug/21 Answered by dumitrel last updated on 18/Aug/21 Commented by dumitrel last updated on 18/Aug/21 Commented by…
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Question Number 150903 by puissant last updated on 16/Aug/21 $${let}\:{x},{y}>\mathrm{0}\:,\:{n}\in\mathbb{N}, \\ $$$${show}\:{that}\:\left({x}+{y}\right)^{{n}} \leqslant\mathrm{2}^{{n}−\mathrm{1}} \left({x}^{{n}} +{y}^{{n}} \right).. \\ $$ Answered by qaz last updated on 16/Aug/21…