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Category: Algebra

Find-the-least-positive-integer-n-for-which-2-n-5-n-n-is-a-multiple-of-1000-

Question Number 160064 by HongKing last updated on 24/Nov/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{least}\:\mathrm{positive}\:\mathrm{integer}\:\:\boldsymbol{\mathrm{n}}\:\:\mathrm{for} \\ $$$$\mathrm{which}\:\:\mathrm{2}^{\boldsymbol{\mathrm{n}}} \:+\:\mathrm{5}^{\boldsymbol{\mathrm{n}}} \:-\:\boldsymbol{\mathrm{n}}\:\:\mathrm{is}\:\mathrm{a}\:\mathrm{multiple}\:\mathrm{of}\:\mathrm{1000} \\ $$ Commented by Rasheed.Sindhi last updated on 24/Nov/21 $$\mathrm{For}\:\mathrm{n}=\mathrm{1000},\:\mathrm{2}^{\boldsymbol{\mathrm{n}}} \:+\:\mathrm{5}^{\boldsymbol{\mathrm{n}}}…

Find-lim-n-1-n-0-1-1-x-n-cosnx-e-x-dx-

Question Number 160063 by HongKing last updated on 24/Nov/21 $$\mathrm{Find}: \\ $$$$\Omega\:=\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{1}}{\mathrm{n}!}\:\underset{\:\mathrm{0}} {\overset{\:\mathrm{1}} {\int}}\:\left(\left(\mathrm{1}\:-\:\mathrm{x}\right)^{\boldsymbol{\mathrm{n}}} \:+\:\mathrm{cos}\boldsymbol{\mathrm{nx}}\right)\mathrm{e}^{\boldsymbol{\mathrm{x}}} \:\mathrm{dx} \\ $$ Terms of Service Privacy Policy Contact:…

Find-n-1-n-1-n-1-2-

Question Number 160062 by HongKing last updated on 24/Nov/21 $$\mathrm{Find}: \\ $$$$\Omega\:=\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\prod}}\left(\frac{\mathrm{n}^{\frac{\mathrm{1}}{\boldsymbol{\mathrm{n}}+\mathrm{1}}} }{\mathrm{2}}\right)\:=\:? \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com