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Question Number 57770 by Tawa1 last updated on 11/Apr/19 Answered by Kunal12588 last updated on 11/Apr/19 $$\underset{{k}=\mathrm{1}} {\overset{\mathrm{13}} {\sum}}\frac{\mathrm{1}}{{sin}\left(\frac{\pi}{\mathrm{4}}+\frac{\left({k}−\mathrm{1}\right)\pi}{\mathrm{6}}\right){sin}\left(\frac{\pi}{\mathrm{4}}+\frac{{k}\pi}{\mathrm{6}}\right)} \\ $$$${sin}\left(\frac{\pi}{\mathrm{4}}+\frac{\left({k}−\mathrm{1}\right)\pi}{\mathrm{6}}\right){sin}\left(\frac{\pi}{\mathrm{4}}+\frac{{k}\pi}{\mathrm{6}}\right) \\ $$$$={sin}\left(\frac{\mathrm{3}\pi+\mathrm{2}\left({k}−\mathrm{1}\right)\pi}{\mathrm{12}}\right){sin}\left(\frac{\mathrm{3}\pi+\mathrm{2}{k}\pi}{\mathrm{12}}\right) \\ $$$$={sin}\left(\frac{\left(\mathrm{2}{k}+\mathrm{1}\right)\pi}{\mathrm{12}}\right){sin}\left(\frac{\left(\mathrm{2}{k}+\mathrm{3}\right)\pi}{\mathrm{12}}\right)…
Question Number 123304 by mordo last updated on 24/Nov/20 $${gcd}\left({a};{b}\right)+{lcm}\left({a};{b}\right)=\mathrm{111} \\ $$$${find}\:{a}\:{and}\:{b} \\ $$ Commented by mr W last updated on 24/Nov/20 $${a}=\mathrm{1} \\ $$$${b}=\mathrm{110}…
Question Number 188796 by Rupesh123 last updated on 07/Mar/23 Commented by mr W last updated on 07/Mar/23 $${consider}\:{your}\:{question}: \\ $$$${f}\left({n}\right)\:{should}\:{be}\:{divisible}\:{by}\:{n}.\:{but} \\ $$$${the}\:{examples}\:{you}\:{gave}\:{are}\:{not} \\ $$$${fibonacci}\:{series}\:{and}\:{are}\:{not}\:{divisible} \\…
Question Number 188722 by Rupesh123 last updated on 06/Mar/23 Commented by Rupesh123 last updated on 06/Mar/23 Find the number of rational terms in the binomial expansion of Answered by BaliramKumar last updated on 06/Mar/23 $$\overset{\mathrm{100}}…
Question Number 188564 by BaliramKumar last updated on 03/Mar/23 $$\mathrm{1}×\mathrm{2}+\mathrm{2}×\mathrm{3}+\mathrm{3}×\mathrm{4}+……………+\mathrm{24}×\mathrm{25}\:=\:? \\ $$ Answered by universe last updated on 03/Mar/23 $$\left(\mathrm{1}^{\mathrm{2}} +\mathrm{1}\right)+\left(\mathrm{2}^{\mathrm{2}} +\mathrm{2}\right)+\left(\mathrm{3}^{\mathrm{2}} +\mathrm{3}\right)+……\left(\mathrm{24}^{\mathrm{2}} +\mathrm{24}\right) \\…
Question Number 122954 by mr W last updated on 21/Nov/20 Commented by Dwaipayan Shikari last updated on 21/Nov/20 $${Infinitely}\:\:{many}\:{answers}\:{sir}! \\ $$$${If}\:{they}\:{are}\:{in}\:{a}\:{relation}\:\:{C}=\mathrm{1}+\left({n}−\mathrm{1}\right) \\ $$$${then}\:\mathrm{12}\:{will}\:{cost}\:\mathrm{12}\:\$\:\:\:\left({for}\:{the}\:{people}\:{who}…..\right) \\ $$$${If}\:{they}\:{are}\:{in}\:{a}\:{relation}…
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Question Number 57377 by Tawa1 last updated on 03/Apr/19 $$\mathrm{Can}\:\mathrm{i}\:\mathrm{find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{a}\:\mathrm{product}\:\mathrm{to}\:\mathrm{infinity}\:? \\ $$$$\:\:\:\mathrm{e}.\mathrm{g}\:\:\:\:\:\:\:\mathrm{1}.\mathrm{2}.\mathrm{3}.\mathrm{4}.\mathrm{5}\:….\:\:\:\:\mathrm{infinity} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 188442 by BaliramKumar last updated on 03/Mar/23 $$ \\ $$$${Solve}\:{by}\:{computer}\:{programing} \\ $$$$\left({if}\:{possible}\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{d}<{a}<{b}\:\&\:{c}\:<\:{a},\:{b}>\mathrm{2}{c} \\ $$$$\cancel{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} =\:\mathrm{5}{c}^{\mathrm{2}} +\mathrm{2}{d}^{\mathrm{2}} }\:\:\:\:\:\:\:\:\:\:\:\:\left({a},\:{b},\:{c},\:{d}\:\:\in\:\mathrm{N}\right) \\ $$$${c}^{\mathrm{2}} +{d}^{\mathrm{2}} \:=\:{a}^{\mathrm{2}} \:\:\:\:\:\:\:\:………\left({i}\right)…