Question Number 207042 by necx122 last updated on 04/May/24 $${Prove}\:{that}\:{the}\:{sum}\:{of}\:{a}\:{square}\:{function} \\ $$$${is}\:\frac{{n}\left({n}+\mathrm{1}\right)\left(\mathrm{2}{n}+\mathrm{1}\right)}{\mathrm{6}} \\ $$ Answered by Rasheed.Sindhi last updated on 04/May/24 $${p}\left({n}\right): \\ $$$$\mathrm{1}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}}…
Question Number 207043 by necx122 last updated on 04/May/24 $${Solve}\:{for}\:{the}\:{domain}\:{and}\:{range}\:{of}\:{f}\left({x}\right)\:{if} \\ $$$${f}\left({x}\right)\:=\:\sqrt{\frac{\mathrm{3}{x}−\mathrm{5}}{{x}+\mathrm{3}}} \\ $$ Answered by Frix last updated on 04/May/24 $$\mathrm{1}.\:{x}+\mathrm{3}\neq\mathrm{0} \\ $$$${x}\neq−\mathrm{3} \\…
Question Number 207021 by efronzo1 last updated on 03/May/24 $$\:\:{If}\:\:{a}_{{n}+\mathrm{1}} =\mathrm{2}−\mathrm{5}{a}_{{n}} \:{and}\:{a}_{\mathrm{4}} =\:−\mathrm{8} \\ $$$$\:\:{prove}\:{that}\:{a}_{\mathrm{43}} −{a}_{\mathrm{30}} \:{divisible}\:{by}\:\mathrm{5} \\ $$ Commented by mr W last updated…
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Question Number 207018 by cherokeesay last updated on 03/May/24 Answered by mr W last updated on 03/May/24 Commented by cherokeesay last updated on 03/May/24 $${R}=?…
Question Number 206997 by efronzo1 last updated on 03/May/24 $$\mathrm{Given}\:\mathrm{a}_{\mathrm{n}+\mathrm{1}} =\:\mathrm{3}−\mathrm{6a}_{\mathrm{n}} \:\mathrm{and}\:\mathrm{a}_{\mathrm{4}} =−\mathrm{9} \\ $$$$\:\mathrm{Find}\:\mathrm{a}_{\mathrm{n}} =?\: \\ $$ Answered by mr W last updated on…
Question Number 206999 by efronzo1 last updated on 03/May/24 $$\:\:\:\mathrm{Prove}\:\mathrm{that}\:\mathrm{6}^{\mathrm{20}} −\mathrm{1}\:=\:\mathrm{0}\:\left(\mathrm{mod}\:\mathrm{7}\right) \\ $$ Commented by Frix last updated on 03/May/24 $$\mathrm{Prove}\:\mathrm{that}\:{n}^{\mathrm{2}{k}} −\mathrm{1}=\mathrm{0}\left(\mathrm{mod}\left({n}+\mathrm{1}\right)\right): \\ $$$${n}^{\mathrm{2}{k}} −\mathrm{1}=\left({n}+\mathrm{1}\right)\underset{{j}=\mathrm{1}}…
Question Number 207008 by mr W last updated on 03/May/24 Answered by A5T last updated on 03/May/24 Commented by A5T last updated on 03/May/24 $$\frac{\mathrm{5}}{{BO}}=\frac{\mathrm{6}}{{CO}}\Rightarrow\frac{{BO}}{{CO}}=\frac{\mathrm{5}}{\mathrm{6}};\:{BO}=\mathrm{5}{x};{CO}=\mathrm{6}{x}…
Question Number 206992 by mnjuly1970 last updated on 03/May/24 $$ \\ $$$$\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\: \\ $$ Answered by mr W last updated on 03/May/24 $$−\mathrm{1}\leqslant{x}^{\mathrm{2}}…
Question Number 206993 by necx122 last updated on 03/May/24 $${If}\:{the}\:{nth}\:{term}\:{of}\:{a}\:{sequence}\:{is} \\ $$$${given}\:{by}\:\frac{{n}^{\mathrm{2}} −\mathrm{2}{n}}{\mathrm{4}}\:,{what}\:{is}\:{the}\:{sum}\:{of}\:{n} \\ $$$${terms}\:{of}\:{the}\:{sequence}? \\ $$ Answered by Rasheed.Sindhi last updated on 03/May/24 $$\underset{{k}=\mathrm{1}}…