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} \\ $$$$\mathrm{158b687a}\:\mathrm{where}\:\mathrm{b}\:\mathrm{and}\:\mathrm{a}\:\mathrm{are} \\ $$$$\mathrm{digits}\:\left(\mathrm{a}<\mathrm{b}\right).\:\mathrm{Given}: \\ $$$$\mathrm{N}\equiv\mathrm{2}+\mathrm{a}\left[\mathrm{4}\right]. \\ $$$$\left.\mathrm{1}\right)\:\mathrm{Determinate}\:\mathrm{couples} \\ $$$$\left(\mathrm{a};\mathrm{b}\right)\:\mathrm{such}\:\mathrm{that}\:\mathrm{11}\:\mathrm{divise}\:\mathrm{N}. \\ $$$$\left.\mathrm{2}\right)\:\mathrm{Determinate}\:\mathrm{couples}\:\left(\mathrm{a};\mathrm{b}\right) \\ $$$$\mathrm{such}\:\mathrm{that}\:\mathrm{3}\:\mathrm{and}\:\mathrm{25}\:\mathrm{divise}\:\mathrm{N}. \\…
Question Number 121567 by mathocean1 last updated on 09/Nov/20 $$\mathrm{Hello}\:\mathrm{how}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{this}\: \\ $$$$\mathrm{equation}: \\ $$$$\begin{cases}{\mathrm{3}{x}−{y}\equiv\mathrm{1}\left[\mathrm{5}\right]}\\{{x}+\mathrm{2}{y}\equiv\mathrm{0}\left[\mathrm{5}\right]}\end{cases} \\ $$ Commented by TANMAY PANACEA last updated on 09/Nov/20 $$\left[\mathrm{5}\right]\:\:{what}\:{does}\:\left[\:.\right]\:{means}…
Question Number 187085 by Rupesh123 last updated on 13/Feb/23 Answered by witcher3 last updated on 14/Feb/23 $$\mathrm{S}_{\mathrm{n}} =\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{1}}{\mathrm{n}+\mathrm{k}} \\ $$$$\mathrm{S}_{\mathrm{n}+\mathrm{1}} −\mathrm{S}_{\mathrm{n}} =\underset{\mathrm{k}=\mathrm{1}} {\overset{\mathrm{n}+\mathrm{1}}…
Question Number 55992 by Mikael_Marshall last updated on 07/Mar/19 $$\mathrm{1}\:+\:{x}\:+\:{x}^{\mathrm{2}} \:+\:.\:.\:.\:+\:{x}^{\mathrm{99}} =\mathrm{0} \\ $$$${need}\:{an}\:{explanation}. \\ $$ Commented by mr W last updated on 07/Mar/19 $${if}\:{x}=−\mathrm{1}:…
Question Number 121496 by Lordose last updated on 08/Nov/20 $$\mathrm{Are}\:\mathrm{they}\:\mathrm{equal}? \\ $$$$\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{sin}\left(\mathrm{n}+\mathrm{1}\right)}{\mathrm{n}+\mathrm{1}}\:\mathrm{and}\:\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{sin}\left(\mathrm{n}\right)}{\mathrm{n}} \\ $$ Commented by Dwaipayan Shikari last updated on…