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n-4-2-3-4-n-3-

Question Number 165210 by mkam last updated on 27/Jan/22 $$\underset{\boldsymbol{{n}}=\mathrm{4}} {\overset{\infty} {\sum}}\:\mathrm{2}\:×\:\left(\frac{\mathrm{3}}{\mathrm{4}}\right)^{\boldsymbol{{n}}+\mathrm{3}} \\ $$ Commented by cortano1 last updated on 27/Jan/22 $$\mathrm{2}×\left[\left(\frac{\mathrm{3}}{\mathrm{4}}\right)^{\mathrm{7}} +\left(\frac{\mathrm{3}}{\mathrm{4}}\right)^{\mathrm{8}} +…\:\right]\:=\:\mathrm{2}×\frac{\left(\frac{\mathrm{3}}{\mathrm{4}}\right)^{\mathrm{7}} }{\left(\frac{\mathrm{1}}{\mathrm{4}}\right)}…

Question-99606

Question Number 99606 by bemath last updated on 22/Jun/20 Commented by john santu last updated on 22/Jun/20 $$\mathrm{let}\:\mathrm{M}\:\mathrm{be}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{the}\:\mathrm{students}\:\mathrm{passing} \\ $$$$\mathrm{in}\:\mathrm{Mathematics}\:,\:\mathrm{P}\:\mathrm{be}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{students}\: \\ $$$$\mathrm{passing}\:\mathrm{in}\:\mathrm{Physics}\:\&\:\mathrm{C}\:\mathrm{be}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\: \\ $$$$\mathrm{students}\:\mathrm{passing}\:\mathrm{in}\:\mathrm{Chemistry} \\…

Question-99584

Question Number 99584 by DGmichael last updated on 21/Jun/20 Answered by Rasheed.Sindhi last updated on 22/Jun/20 $${If}\:\:{a}\equiv{b}\left({mod}\:{m}\right)\:{and}\:{P}\left({x}\right)\:{is}\:{a} \\ $$$${polynomial}\:{with}\:{integer}\:{coficients} \\ $$$${then} \\ $$$$\:\:\:\:\:{P}\left({a}\right)\equiv{P}\left({b}\right)\left({mod}\:{m}\right) \\ $$$$…

Prove-that-for-every-positive-real-numbers-x-y-z-and-xyz-1-hold-x-y-z-2-1-x-2-1-y-2-1-z-2-9-2-x-3-y-3-z-3-4-1-x-3-1-y-3-1-z-3-

Question Number 34031 by naka3546 last updated on 29/Apr/18 $${Prove}\:\:{that}\:\:{for}\:\:{every}\:\:{positive}\:\:{real}\:\:{numbers}\:\:{x},\:{y},\:{z}\:\:{and}\:\:\:{xyz}\:\:=\:\:\mathrm{1},\:\:{hold} \\ $$$$\left({x}\:+\:{y}\:+\:{z}\right)^{\mathrm{2}} \left(\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{{y}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{{z}^{\mathrm{2}} }\right)\:\:\geqslant\:\:\mathrm{9}\:+\:\mathrm{2}\left({x}^{\mathrm{3}} \:+\:{y}^{\mathrm{3}} \:+\:{z}^{\mathrm{3}} \right)\:+\:\mathrm{4}\left(\frac{\mathrm{1}}{{x}^{\mathrm{3}} }\:+\:\frac{\mathrm{1}}{{y}^{\mathrm{3}} }\:+\:\frac{\mathrm{1}}{{z}^{\mathrm{3}} }\right)\: \\ $$ Terms…