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Category: Algebra

Find-n-1-ln-n-

Question Number 164240 by HongKing last updated on 15/Jan/22 $$\mathrm{Find}:\:\:\:\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\:\mathrm{ln}\:\left(\mathrm{n}\right)\:=\:? \\ $$ Answered by mathmax by abdo last updated on 15/Jan/22 $$\mathrm{this}\:\mathrm{serie}\:\mathrm{diverges}\:\mathrm{to}\:+\infty \\…

Evalute-the-sum-k-1-n-k-pi-n-2-arctan-kpi-n-2-

Question Number 164196 by HongKing last updated on 15/Jan/22 $$\mathrm{Evalute}\:\mathrm{the}\:\mathrm{sum}: \\ $$$$\underset{\boldsymbol{\mathrm{k}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{n}}} {\sum}}\:\mathrm{k}\:\left(\frac{\pi}{\mathrm{n}}\right)^{\mathrm{2}} \mathrm{arctan}\:\left(\frac{\mathrm{k}\pi}{\mathrm{n}}\right)^{\mathrm{2}} \\ $$ Answered by mathmax by abdo last updated on…

Question-164193

Question Number 164193 by mathlove last updated on 15/Jan/22 Commented by MJS_new last updated on 15/Jan/22 $${x},\:{y},\:{z}\:\mathrm{can}\:\mathrm{be}\:>\mathrm{0}\:\mathrm{or}\:<\mathrm{0} \\ $$$$\Rightarrow \\ $$$$\mathrm{answer}\:\mathrm{is}\:\mathrm{3}\:\mathrm{or}\:\frac{\mathrm{1}}{\mathrm{300}} \\ $$ Commented by…

if-ABC-is-a-triangle-with-usual-notations-then-prove-the-following-inequality-4R-r-3-4r-2-2R-r-3s-2-2R-r-0-

Question Number 164156 by HongKing last updated on 14/Jan/22 $$\mathrm{if}\:\:\mathrm{ABC}\:\:\mathrm{is}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{with}\:\mathrm{usual} \\ $$$$\mathrm{notations},\:\mathrm{then}\:\mathrm{prove}\:\mathrm{the}\:\mathrm{following} \\ $$$$\mathrm{inequality}: \\ $$$$\left(\mathrm{4R}\:+\:\mathrm{r}\right)^{\mathrm{3}} \:-\:\mathrm{4r}^{\mathrm{2}} \left(\mathrm{2R}\:-\:\mathrm{r}\right)\:-\:\mathrm{3s}^{\mathrm{2}} \left(\mathrm{2R}\:+\:\mathrm{r}\right)\:\geqslant\:\mathrm{0} \\ $$ Terms of Service Privacy…

let-a-b-c-0-and-ab-bc-ca-2abc-1-find-min-value-of-S-S-a-1-b-1-c-1-

Question Number 164157 by HongKing last updated on 14/Jan/22 $$\mathrm{let}\:\:\mathrm{a};\mathrm{b};\mathrm{c}\geqslant\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{ab}+\mathrm{bc}+\mathrm{ca}+\mathrm{2abc}\geqslant\mathrm{1} \\ $$$$\mathrm{find}\:\boldsymbol{\mathrm{min}}\:-\:\mathrm{value}\:\mathrm{of}\:\boldsymbol{\mathrm{S}} \\ $$$$\boldsymbol{\mathrm{S}}\:=\:\sqrt{\mathrm{a}\:+\:\mathrm{1}}\:+\:\sqrt{\mathrm{b}\:+\:\mathrm{1}}\:+\:\sqrt{\mathrm{c}\:+\:\mathrm{1}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

x-2-xy-y-2-9-y-2-yz-z-2-16-x-2-xz-z-2-25-Find-S-xy-yz-xz-

Question Number 164154 by HongKing last updated on 14/Jan/22 $$\begin{cases}{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{xy}\:+\:\mathrm{y}^{\mathrm{2}} \:=\:\mathrm{9}}\\{\mathrm{y}^{\mathrm{2}} \:+\:\mathrm{yz}\:+\:\mathrm{z}^{\mathrm{2}} \:=\:\mathrm{16}}\\{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{xz}\:+\:\mathrm{z}^{\mathrm{2}} \:=\:\mathrm{25}}\end{cases} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{S}\:=\:\mathrm{xy}\:+\:\mathrm{yz}\:+\:\mathrm{xz} \\ $$ Answered by behi834171 last updated…