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Question Number 160833 by Raxreedoroid last updated on 07/Dec/21 $$\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{cos}\:\left(\mathrm{ln}\:{k}\right)}{\:\sqrt{{k}}} \\ $$$$\mathrm{divergespnt}\:\mathrm{or}\:\mathrm{convergent}? \\ $$ Answered by mathmax by abdo last updated on 07/Dec/21…
Question Number 29645 by gyugfeet last updated on 11/Feb/18 $${if}\:{the}\:{sum}\:{of}\:{first}\:\mathrm{5}\:{terms}\:{of}\:\:{a}\:{G}.{P}.\:{is}\:\mathrm{155},\:{sum}\:{of}\:{last}\:\mathrm{5}\:{terms}\:{is}\:\mathrm{39680},{first}\:{term}\:{is}\:\mathrm{5}\:{and}\:{last}\:{term}\:\:{is}\:\mathrm{20480}.\:{find}\:{the}\:{number}\:{of}\:{terms}\:{of}\:{the}\:{sequence}. \\ $$ Answered by Rasheed.Sindhi last updated on 11/Feb/18 $$\mathrm{Let}\:\mathrm{the}\:\mathrm{common}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{the}\:\mathrm{GP}\:\mathrm{is}\:\mathrm{r} \\ $$$$\mathrm{Sum}\:\mathrm{of}\:\mathrm{first}\:\mathrm{five}\:\mathrm{terms}: \\ $$$$\mathrm{5}+\mathrm{5r}+\mathrm{5r}^{\mathrm{2}} +\mathrm{5r}^{\mathrm{3}}…
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Question Number 94925 by I want to learn more last updated on 21/May/20 Commented by mr W last updated on 22/May/20 $${AB}={AC}={BC}={Radius} \\ $$$$\Rightarrow\Delta{ABC}={equilateral} \\…
Question Number 94921 by peter frank last updated on 21/May/20 Answered by Kunal12588 last updated on 22/May/20 Commented by Kunal12588 last updated on 22/May/20 Commented…
Question Number 160350 by Lekhraj last updated on 28/Nov/21 Answered by Rasheed.Sindhi last updated on 28/Nov/21 $$\mathrm{2001}\:\:\:\:\:{Let}\:{ages}\:{were}\:{x}\:\&\:\mathrm{11}{x} \\ $$$$\mathrm{2018}\:\:\:\:\:\:{x}+\mathrm{17}:\mathrm{11}{x}+\mathrm{17}=\mathrm{2}:\mathrm{5} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{5}\left({x}+\mathrm{17}\right)=\mathrm{2}\left(\mathrm{11}{x}+\mathrm{17}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{5}{x}+\mathrm{85}=\mathrm{22}{x}+\mathrm{34} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{17}{x}=\mathrm{51}\Rightarrow{x}=\mathrm{3}…
Question Number 29169 by abdo imad last updated on 04/Feb/18 $${factorize}\:{inside}\:{R}\left[{x}\right]\:{the}\:{polynomial} \\ $$$${p}\left({x}\right)=\:{x}^{\mathrm{8}} −\mathrm{1}. \\ $$ Commented by abdo imad last updated on 06/Feb/18 $${p}\left({x}\right)=\left({x}^{\mathrm{4}}…
Question Number 29163 by abdo imad last updated on 04/Feb/18 $${let}\:{give}\:\left({n},{p}\right)\:{from}\:{N}^{\mathrm{2}} \:{and}\:\mathrm{1}\leqslant{p}\leqslant{n}\:{prove}\:{that}\: \\ $$$$\sum_{{k}=\mathrm{0}} ^{{p}} \:{C}_{{n}} ^{{k}} \:{C}_{{n}−{k}} ^{{p}−{k}} ==\mathrm{2}^{{p}} \:\:{C}_{{n}} ^{{p}} . \\ $$$$…
Question Number 94602 by peter frank last updated on 19/May/20 Answered by mr W last updated on 21/May/20 Commented by mr W last updated on…