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Author: Tinku Tara

k-0-n-n-k-1-

Question Number 221382 by MrGaster last updated on 02/Jun/25 $$\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\begin{pmatrix}{{n}}\\{{k}}\end{pmatrix}^{−\mathrm{1}} \\ $$ Commented by mr W last updated on 05/Jun/25 $$=\frac{\mathrm{1}}{{n}!}\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}{k}!\left({n}−{k}\right)!…

Question-221373

Question Number 221373 by Nicholas666 last updated on 01/Jun/25 Commented by MathematicalUser2357 last updated on 09/Jun/25 $$\frac{\frac{\int_{\mathrm{0}} ^{\infty} \mathrm{cos}\:\frac{\mathrm{3}\sqrt{\mathrm{3}}}{\mathrm{4}}{x}^{\mathrm{3}} {dx}}{\int_{\mathrm{0}} ^{\infty} \mathrm{sin}\:\mathrm{16}{x}^{\mathrm{3}} {dx}}+\left(\int_{\mathrm{0}} ^{\infty} \mathrm{ln}\left(\frac{\left(\mathrm{1}+\mathrm{2}{x}^{\mathrm{2}\sqrt{\mathrm{2}}}…

Find-lim-n-2-10-1-n-1-n-

Question Number 221377 by hardmath last updated on 01/Jun/25 $$\mathrm{Find}:\:\:\:\Omega\:=\underset{\boldsymbol{\mathrm{n}}\rightarrow\infty} {\mathrm{lim}}\:\left(\mathrm{2}\:\sqrt[{\boldsymbol{\mathrm{n}}}]{\mathrm{10}}\:−\:\mathrm{1}\right)^{\boldsymbol{\mathrm{n}}} \:=\:? \\ $$ Answered by Ghisom last updated on 01/Jun/25 $$\mathrm{ln}\:\Omega\:=\underset{{n}\rightarrow\infty} {\mathrm{lim}}\:{n}\mathrm{ln}\:\left(\mathrm{2}×\mathrm{10}^{\mathrm{1}/{n}} −\mathrm{1}\right) \\…