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Author: Tinku Tara

4n-2-2n-e-n-

Question Number 150135 by Gbenga last updated on 09/Aug/21 $$\mathrm{4}{n}^{\mathrm{2}} +\mathrm{2}{n}={e}^{{n}} \\ $$ Answered by MJS_new last updated on 10/Aug/21 $$\mathrm{you}\:\mathrm{can}\:\mathrm{only}\:\mathrm{approximate} \\ $$$${n}\approx−.\mathrm{684294}\vee{n}\approx\mathrm{4}.\mathrm{49967} \\ $$…

Question-19060

Question Number 19060 by mondodotto@gmail.com last updated on 03/Aug/17 Commented by prakash jain last updated on 04/Aug/17 $${can}\:{u}\:{please}\:{use}\:{an}\:{app}\:{called} \\ $$$${camscanner}\:{to}\:{take}\:{clear}\:{images} \\ $$$${of}\:{handwritten}\:{or}\:{printed}\:{material}. \\ $$ Commented…

Find-the-cubic-equation-whose-roots-are-the-radius-of-three-escribed-circles-in-term-of-inradius-circumradius-and-semiperimeter-

Question Number 19055 by Tinkutara last updated on 03/Aug/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{cubic}\:\mathrm{equation}\:\mathrm{whose}\:\mathrm{roots} \\ $$$$\mathrm{are}\:\mathrm{the}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{three}\:\mathrm{escribed}\:\mathrm{circles} \\ $$$$\mathrm{in}\:\mathrm{term}\:\mathrm{of}\:\mathrm{inradius},\:\mathrm{circumradius}\:\mathrm{and} \\ $$$$\mathrm{semiperimeter}. \\ $$ Answered by behi.8.3.4.1.7@gmail.com last updated on 05/Aug/17…

Find-the-sum-1-2-1-3-1-4-1-5-1-6-1-7-1-8-1-9-

Question Number 19053 by Tinkutara last updated on 03/Aug/17 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}:\:\frac{\mathrm{1}}{\mathrm{2}}\:−\:\frac{\mathrm{1}}{\mathrm{3}}\:+\:\frac{\mathrm{1}}{\mathrm{4}}\:−\:\frac{\mathrm{1}}{\mathrm{5}}\:+\:\frac{\mathrm{1}}{\mathrm{6}} \\ $$$$−\:\frac{\mathrm{1}}{\mathrm{7}}\:+\:\frac{\mathrm{1}}{\mathrm{8}}\:−\:\frac{\mathrm{1}}{\mathrm{9}}\:+\:… \\ $$ Answered by ajfour last updated on 03/Aug/17 $$\mathrm{ln}\:\left(\mathrm{1}+\mathrm{x}\right)=\mathrm{x}−\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{2}}+\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{3}}−\frac{\mathrm{x}^{\mathrm{4}} }{\mathrm{4}}+\frac{\mathrm{x}^{\mathrm{5}}…

Find-in-closed-form-n-N-0-1-ln-1-x-2-ln-n-1-x-dx-

Question Number 150121 by mathdanisur last updated on 09/Aug/21 $$\mathrm{Find}\:\mathrm{in}\:\mathrm{closed}\:\mathrm{form}:\:\:\mathrm{n}\in\mathbb{N}^{\ast} \\ $$$$\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:\mathrm{ln}\left(\mathrm{1}\:-\:\mathrm{x}^{\mathrm{2}} \right)\mathrm{ln}^{\boldsymbol{\mathrm{n}}} \left(\mathrm{1}\:-\:\mathrm{x}\right)\:\mathrm{dx}\:=\:? \\ $$ Answered by Kamel last updated on 09/Aug/21…