Question Number 187619 by BaliramKumar last updated on 19/Feb/23 $$\mathrm{32}^{\mathrm{32}^{\mathrm{32}} } \:\equiv\:{r}\:\left({mod}\:\:\:\mathrm{7}\right) \\ $$$${r}\:=\:? \\ $$ Answered by SEKRET last updated on 19/Feb/23 $$\left(\mathrm{32}\right)^{\mathrm{32}^{\mathrm{32}} }…
Question Number 122036 by physicstutes last updated on 13/Nov/20 $$\mathrm{Let}\:\:{f}\left({x}\right)\:=\:\left(\frac{{x}+\mathrm{1}}{{x}+\mathrm{2}}\right)\:\mathrm{and}\:\underset{{r}=\mathrm{0}} {\overset{\infty} {\sum}}\left[{f}\left({x}\right)\right]^{{r}} \:\mathrm{be}\:\mathrm{a}\:\mathrm{convergent}\:\mathrm{series} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{x}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left[\underset{{r}=\mathrm{0}} {\overset{\infty} {\sum}}\left(\frac{{x}+\mathrm{1}}{{x}+\mathrm{2}}\right)^{{r}} \right]^{{n}} \:=\:\mathrm{4}\: \\ $$…
Question Number 187560 by Mingma last updated on 18/Feb/23 Answered by mr W last updated on 19/Feb/23 $${i}\:{think}\:{there}\:{is}\:{only}\:{one}\:{possibility}. \\ $$$${blue}\:{numbers}\:{show}\:{the}\:{order}\:{in}\:{which} \\ $$$${i}\:{determined}\:{the}\:{red}\:{numbers}. \\ $$$$\mathrm{62}/\mathrm{2}=\mathrm{31}\:\:\left(\mathrm{2}\right) \\…
Question Number 121949 by liberty last updated on 12/Nov/20 $$\:\mathrm{Evaluate}\:\mathrm{the}\:\mathrm{sum}\:\:\frac{\mathrm{2}}{\mathrm{3}+\mathrm{1}}\:+\:\frac{\mathrm{2}^{\mathrm{2}} }{\mathrm{3}^{\mathrm{2}} +\mathrm{1}}\:+\:\frac{\mathrm{2}^{\mathrm{3}} }{\mathrm{3}^{\mathrm{4}} +\mathrm{1}}+\:…+\:\frac{\mathrm{2}^{\mathrm{n}+\mathrm{1}} }{\mathrm{3}^{\mathrm{2}^{\mathrm{n}} } \:+\mathrm{1}}\:. \\ $$ Answered by bobhans last updated on…
Question Number 187390 by mathlove last updated on 18/Feb/23 $${odd}\:{number}\:\left(\mathrm{2}{n}+\mathrm{1}\right) \\ $$The sum of twelve consecutive natural numbers is 288. Find the largest natural number…
Question Number 121832 by bemath last updated on 12/Nov/20 $$\:\:{Let}\:\begin{cases}{{u}_{\mathrm{1}} =\mathrm{1}}\\{{u}_{\mathrm{2}} =\mathrm{1}}\end{cases}\:{and}\:{u}_{{n}+\mathrm{2}} \:=\:{u}_{{n}+\mathrm{1}} \:+\:{u}_{{n}} \\ $$$${find}\:{u}_{{n}} . \\ $$ Commented by bemath last updated on…
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Question Number 187235 by Rupesh123 last updated on 15/Feb/23 Commented by MJS_new last updated on 15/Feb/23 $$\mathrm{I}\:\mathrm{believe}\:\mathrm{it}'\mathrm{s}\:\mathrm{3} \\ $$ Commented by Rasheed.Sindhi last updated on…
Question Number 56146 by gunawan last updated on 11/Mar/19 $$\mathrm{Given}\:\mathrm{complex}\:\mathrm{number} \\ $$$${z}_{\mathrm{1}} ,\:{z}_{\mathrm{2}} ,\:\mathrm{and}\:{z}_{\mathrm{3}} \:\mathrm{satiesfied}\:{z}_{\mathrm{1}} +{z}_{\mathrm{2}} +{z}_{\mathrm{3}} =\mathrm{0} \\ $$$$\mathrm{and}\:\mid{z}_{\mathrm{1}} \mid=\mid{z}_{\mathrm{2}} \mid=\mid{z}_{\mathrm{3}} \mid=\mathrm{1}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$${z}_{\mathrm{1}}…
Question Number 121568 by mathocean1 last updated on 09/Nov/20 $$\mathrm{Given}:\:\mathrm{N}\:\mathrm{in}\:\mathrm{base}\:\mathrm{10}\:\mathrm{is} \\ $$$$\mathrm{158b687a}\:\mathrm{where}\:\mathrm{b}\:\mathrm{and}\:\mathrm{a}\:\mathrm{are} \\ $$$$\mathrm{digits}\:\left(\mathrm{a}<\mathrm{b}\right).\:\mathrm{Given}: \\ $$$$\mathrm{N}\equiv\mathrm{2}+\mathrm{a}\left[\mathrm{4}\right]. \\ $$$$\left.\mathrm{1}\right)\:\mathrm{Determinate}\:\mathrm{couples} \\ $$$$\left(\mathrm{a};\mathrm{b}\right)\:\mathrm{such}\:\mathrm{that}\:\mathrm{11}\:\mathrm{divise}\:\mathrm{N}. \\ $$$$\left.\mathrm{2}\right)\:\mathrm{Determinate}\:\mathrm{couples}\:\left(\mathrm{a};\mathrm{b}\right) \\ $$$$\mathrm{such}\:\mathrm{that}\:\mathrm{3}\:\mathrm{and}\:\mathrm{25}\:\mathrm{divise}\:\mathrm{N}. \\…