Menu Close

Category: Algebra

find-the-sum-of-the-first-n-terms-from-1-2-3-4-5-6-7-8-9-10-

Question Number 198243 by mr W last updated on 15/Oct/23 $${find}\:{the}\:{sum}\:{of}\:{the}\:{first}\:{n}\:{terms}\:{from} \\ $$$$\mathrm{1},\:\mathrm{2}+\mathrm{3},\:\mathrm{4}+\mathrm{5}+\mathrm{6},\:\mathrm{7}+\mathrm{8}+\mathrm{9}+\mathrm{10},\:… \\ $$ Answered by som(math1967) last updated on 15/Oct/23 $$\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}+\mathrm{5}+\mathrm{6}+\mathrm{7}+\mathrm{8}+\mathrm{9}+\mathrm{10}+..{n} \\ $$$${no}\:{of}\:{term}\:=\frac{{n}\left({n}+\mathrm{1}\right)}{\mathrm{2}}…

Prove-The-following-Functional-equation-x-s-2-1-s-2pi-1-s-sin-pis-2-m-1-cos-2pimx-m-1-s-cos-pis-2-m-1-sin-2pimx-m-1-s-

Question Number 198175 by York12 last updated on 12/Oct/23 $${Prove}\:{The}\:{following}\:{Functional}\:{equation}: \\ $$$$\zeta\left({x},{s}\right)=\frac{\mathrm{2}\Gamma\left(\mathrm{1}−{s}\right)}{\left(\mathrm{2}\pi\right)^{\left(\mathrm{1}−{s}\right)} }\left\{{sin}\left(\frac{\pi{s}}{\mathrm{2}}\right)\underset{{m}=\mathrm{1}} {\overset{\infty} {\sum}}\left[\frac{{cos}\left(\mathrm{2}\pi{mx}\right)}{{m}^{\left(\mathrm{1}−{s}\right)} }\right]+{cos}\left(\frac{\pi{s}}{\mathrm{2}}\right)\underset{{m}=\mathrm{1}} {\overset{\infty} {\sum}}\left[\frac{{sin}\left(\mathrm{2}\pi{mx}\right)}{{m}^{\left(\mathrm{1}−{s}\right)} }\right]\right\} \\ $$ Answered by witcher3 last…

Solve-log-x-2-7x-5-log-x-2-2-

Question Number 198132 by a.lgnaoui last updated on 11/Oct/23 $${Solve}: \\ $$$$\frac{\boldsymbol{\mathrm{log}}\left(\boldsymbol{\mathrm{x}}^{\mathrm{2}} +\mathrm{7}\boldsymbol{\mathrm{x}}−\mathrm{5}\right)}{\boldsymbol{\mathrm{log}}\left(\boldsymbol{\mathrm{x}}+\mathrm{2}\right)}=\mathrm{2} \\ $$ Answered by som(math1967) last updated on 11/Oct/23 $${log}\left({x}^{\mathrm{2}} +\mathrm{7}{x}−\mathrm{5}\right)=\mathrm{2}{log}\left({x}+\mathrm{2}\right) \\…

Resoudre-log-x-3-log-x-2-log-x-2-4x-21-

Question Number 198131 by a.lgnaoui last updated on 11/Oct/23 $$\mathrm{Resoudre} \\ $$$$\boldsymbol{\mathrm{log}}\left(\boldsymbol{\mathrm{x}}−\mathrm{3}\right)+\boldsymbol{\mathrm{log}}\left(\boldsymbol{\mathrm{x}}−\mathrm{2}\right)=\boldsymbol{\mathrm{log}}\left(\boldsymbol{\mathrm{x}}^{\mathrm{2}} −\mathrm{4}\boldsymbol{\mathrm{x}}−\mathrm{21}\right) \\ $$$$ \\ $$ Answered by Rasheed.Sindhi last updated on 11/Oct/23 $$\mathrm{log}\left(\mathrm{x}−\mathrm{3}\right)+\mathrm{log}\left(\mathrm{x}−\mathrm{2}\right)=\mathrm{log}\left(\mathrm{x}^{\mathrm{2}}…

solve-for-x-y-N-x-y-2023-

Question Number 198103 by mr W last updated on 10/Oct/23 $${solve}\:{for}\:{x},\:{y}\:\in{N} \\ $$$$\sqrt{{x}}+\sqrt{{y}}=\sqrt{\mathrm{2023}} \\ $$ Answered by Safojon last updated on 10/Oct/23 $$\sqrt{\mathrm{7}}+\mathrm{16}\sqrt{\mathrm{7}}=\sqrt{\mathrm{2023}} \\ $$$$\mathrm{2}\sqrt{\mathrm{7}}+\mathrm{15}\sqrt{\mathrm{7}}=\sqrt{\mathrm{2023}}…