Category: Algebra

Question Number 203774 by Calculusboy last updated on 27/Jan/24 $$\mathit{d}\mathit{e}\mathit{t}\mathit{e}\mathit{r}\mathit{m}\mathit{i}\mathit{n}\mathit{e}\mathit{w}\mathit{h}\mathit{e}\mathit{t}\mathit{h}\mathit{e}\mathit{r}\mathit{t}\mathit{h}\mathit{e}\mathit{s}\mathit{e}\mathit{r}\mathit{i}\mathit{e}\mathit{s}\mathit{i}\mathit{s}$$$$\mathit{c}\mathit{o}\mathit{n}\mathit{v}\mathit{e}\mathit{r}\mathit{g}\mathit{e}\mathit{n}\mathit{t}\mathit{o}\mathit{r}\mathit{d}\mathit{i}\mathit{v}\mathit{e}\mathit{r}\mathit{g}\mathit{e}\mathit{n}\mathit{t}$$$$\underset{\mathit{n}=1}{\mathbf{\sum }^{\mathrm{\infty }}}\frac{\mathit{n}}{\sqrt{4{\mathit{n}}^2+1}}$$ Answered by witcher3 last updated on…

Question Number 203771 by Calculusboy last updated on 27/Jan/24 Answered by DwaipayanShikari last updated on 27/Jan/24 $$\underset{n=0}{\sum ^{\mathrm{\infty }}}\frac{1}{\left(\begin{array}{c}n+3\\ 3\end{array}\right)}$$$$=\underset{n=0}{\sum ^{\mathrm{\infty }}}\frac{n!}{(n+3)!3!}$$$$=\frac{\mathrm{1}}{\mathrm{3}!}\underset{{n}=\mathrm{0}}…

Question Number 203570 by Frix last updated on 22/Jan/24 $$\mathrm{Suggested}\mathrm{solution}\mathrm{method}\mathrm{to}$$$$\mathrm{question}203502$$$$$$$$z{\mathrm{e}}^z=1$$$$\mathrm{Obviously}\mathrm{the}\mathrm{only}\mathrm{real}\mathrm{solution}\mathrm{is}$$$$z=W\left(1\right)\approx .567143290$$$$$$$${z}={a}+{b}\mathrm{i}\wedge{b}\neq\mathrm{0}…

Question Number 203502 by Frix last updated on 20/Jan/24 $$z{\mathrm{e}}^z=\mathrm{e}$$$$\mathrm{Obviously}z=1$$$$\mathrm{Now}\mathrm{find}\mathrm{at}\mathrm{least}\mathrm{one}\mathrm{solution}\mathrm{for}z\in \mathbb{C}$$ Commented by Frix last updated on 22/Jan/24 $$\mathrm{See}\:\mathrm{question}\:\mathrm{203570}…

Question Number 203448 by hardmath last updated on 19/Jan/24 $$\mathrm{y}=\sin 3\mathrm{x}-\ln (3\mathrm{x}+1)+3^{2\mathbf{x}}$$$$\mathrm{find}:{\mathrm{y}}^{{}^{\prime }}=?$$ Commented by hardmath last updated on 19/Jan/24 $$$$find…