Question Number 151956 by mathdanisur last updated on 24/Aug/21 $$\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:\underset{\boldsymbol{\mathrm{k}}=\mathrm{1}} {\overset{\boldsymbol{\mathrm{n}}} {\sum}}\:\mathrm{arctan}\:\frac{\mathrm{1}}{\mathrm{2k}^{\mathrm{2}} }\:\mathrm{arctan}\:\frac{\mathrm{2k}^{\mathrm{2}} \:-\:\mathrm{1}}{\mathrm{2k}^{\mathrm{2}} }\:=\:? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 86426 by M±th+et£s last updated on 28/Mar/20 $${solve}\:{in}\:{R} \\ $$$${x}^{\mathrm{3}} −\mathrm{5}=\left[{x}\right] \\ $$ Answered by mr W last updated on 28/Mar/20 $${let}\:{x}={n}+\delta \\…
Question Number 20882 by soufiane zarik last updated on 06/Sep/17 Answered by $@ty@m last updated on 08/Sep/17 Commented by soufiane zarik last updated on 11/Sep/17…
Question Number 20881 by tawa tawa last updated on 05/Sep/17 Answered by mrW1 last updated on 06/Sep/17 $$\left(\mathrm{ax}+\mathrm{ay}\right)^{\mathrm{n}} =\mathrm{a}^{\mathrm{n}} \left(\mathrm{x}+\mathrm{y}\right)^{\mathrm{n}} \\ $$$$\mathrm{since}\:\mathrm{a}\:\mathrm{middle}\:\mathrm{term}\:\mathrm{exists},\:\mathrm{n}\:\mathrm{is}\:\mathrm{even}. \\ $$$$\mathrm{its}\:\mathrm{middle}\:\mathrm{term}\:\mathrm{is} \\…
Question Number 151948 by mathdanisur last updated on 24/Aug/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
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Question Number 20867 by Tinkutara last updated on 05/Sep/17 $$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{irrational}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{equation} \\ $$$$\left({x}\:−\:\mathrm{1}\right)\left({x}\:−\:\mathrm{2}\right)\left(\mathrm{3}{x}\:−\:\mathrm{2}\right)\left(\mathrm{3}{x}\:+\:\mathrm{1}\right)\:=\:\mathrm{21}\:\mathrm{is} \\ $$ Answered by alex041103 last updated on 09/Sep/17 $$\left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right)\left(\mathrm{3}{x}−\mathrm{2}\right)\left(\mathrm{3}{x}+\mathrm{1}\right)= \\…
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Question Number 151921 by mathdanisur last updated on 24/Aug/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 151911 by mathdanisur last updated on 24/Aug/21 $$\mathrm{Determine}\:\mathrm{the}\:\mathrm{digit}\:\boldsymbol{\mathrm{a}}\:\mathrm{and}\:\mathrm{prime} \\ $$$$\mathrm{numbers}\:\boldsymbol{\mathrm{x}};\boldsymbol{\mathrm{y}};\boldsymbol{\mathrm{z}}\:\mathrm{such}\:\mathrm{that}\:\boldsymbol{\mathrm{x}}<\boldsymbol{\mathrm{y}},\:\boldsymbol{\mathrm{z}}<\mathrm{1000} \\ $$$$\mathrm{and}\:\:\mathrm{x}\:+\:\mathrm{y}^{\mathrm{2}\boldsymbol{\mathrm{a}}} \:=\:\mathrm{z} \\ $$ Commented by Rasheed.Sindhi last updated on 24/Aug/21 $$\mathrm{2}\boldsymbol{\mathrm{a}}\:{means}\:\mathrm{20},\mathrm{21},\mathrm{22},…,\mathrm{29}?\:{Or}\:\mathrm{2}\boldsymbol{\mathrm{a}}=\mathrm{2}×\boldsymbol{\mathrm{a}}?…