Category: Algebra

Question Number 28432 by abdo imad last updated on 25/Jan/18 $$letputw=e^{i\frac{2\pi }{n}}calculate{S}_n=\sum _{k=0}^{n-1}\frac{1}{x-w^k}and$$$$W_n=\sum _{k=0}^{n-1}\frac{1}{{(x-w^k)}^2}.$$…

Question Number 159493 by HongKing last updated on 17/Nov/21 Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 159494 by HongKing last updated on 17/Nov/21 Answered by qaz last updated on 18/Nov/21 $$(1+\mathrm{a})(1+\frac{\mathrm{b}}{\mathrm{a}})(1+\frac{\mathrm{c}}{\mathrm{b}})(1+\frac{81}{\mathrm{c}})$$$$⩾{(1+\sqrt{\mathrm{a}}\cdot \sqrt{\frac{\mathrm{b}}{\mathrm{a}}})}^2{(1+\sqrt{\frac{\mathrm{c}}{\mathrm{b}}}\cdot \sqrt{\frac{81}{\mathrm{c}}})}^2$$$$={(1+\sqrt{\mathrm{b}})}^2{(1+\sqrt{\frac{81}{\mathrm{b}}})}^2$$$$\geqslant\left(\mathrm{1}+\sqrt[{\mathrm{4}}]{\mathrm{b}}\centerdot\sqrt[{\mathrm{4}}]{\frac{\mathrm{81}}{\mathrm{b}}}\right)^{\mathrm{4}}…

Question Number 159490 by akolade last updated on 17/Nov/21 Commented by Rasheed.Sindhi last updated on 18/Nov/21 $$Whynotinoneline?$$ Terms of Service Privacy Policy Contact:…

Question Number 159479 by quvonnn last updated on 17/Nov/21 Answered by Tokugami last updated on 17/Nov/21 $$\frac{2}{4\times 2!}+\frac{2}{5\times 3!}+\frac{2}{6\times 4!}+\frac{2}{7\times 5!}+\frac{2}{8\times 6!}+\dots$$$$=\underset{n=2}{\sum ^{\mathrm{\infty }}}\frac{2}{(n+2)n!}$$$$=\mathrm{2}\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{\mathrm{1}\left({n}+\mathrm{1}\right)}{\left({n}+\mathrm{2}\right)\left({n}+\mathrm{1}\right){n}!}…