Category: Algebra

Question Number 155420 by amin96 last updated on 30/Sep/21 $$\frac{1}{42}+\frac{1}{72}+\frac{1}{110}+\dots =?$$ Answered by puissant last updated on 01/Oct/21 $$S=\frac{1}{42}+\frac{1}{72}+\frac{1}{110}+\dots \dots .=\frac{1}{6}-\frac{1}{7}+\frac{1}{8}-\frac{1}{9}+\dots .$$$$\Rightarrow\:{S}=\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left(\mathrm{2}{n}+\mathrm{2}\right)\left(\mathrm{2}{n}+\mathrm{3}\right)}=\frac{\mathrm{1}}{\mathrm{4}}\underset{{n}=\mathrm{2}} {\overset{\infty}…

Question Number 155386 by mathdanisur last updated on 29/Sep/21 $$\mathrm{Prove}\mathrm{that}:$$$$\underset{\mathbf{k}=1}{\sum ^{\mathrm{\infty }}}\frac{{\left({\mathrm{H}}_{\mathbf{k}}\right)}^3}{2^{\mathbf{k}}}=\frac{3\zeta \left(3\right)+{\ln }^{3}2+{\pi }^2\ln 2}{3}$$ Answered by Kamel last…

Question Number 155372 by mathdanisur last updated on 29/Sep/21 Commented by Rasheed.Sindhi last updated on 30/Sep/21 $${What}^{\prime }smeantby\mathrm{Z}.\mathrm{Q}?$$ Commented by mathdanisur last updated on…

Question Number 89829 by student work last updated on 19/Apr/20 Commented by MJS last updated on 19/Apr/20 English please / Français s'il vous plaît Commented by student work last updated on…

Question Number 155362 by mathdanisur last updated on 29/Sep/21 $$\mathrm{if}\mathrm{a};\mathrm{b}⩾0\mathrm{and}{\mathrm{a}}^4+{\mathrm{b}}^4=17\mathrm{prove}\mathrm{that}:$$$$15(\mathrm{a}+\mathrm{b})⩾17+14\sqrt{2\mathrm{ab}}$$$$$$ Terms of Service Privacy Policy Contact: info@tinkutara.com