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Category: Arithmetic

Question-81222

Question Number 81222 by M±th+et£s last updated on 10/Feb/20 Answered by mind is power last updated on 10/Feb/20 $$\:\:_{\mathrm{1}} {F}_{{a}} \left(\mathrm{1};\frac{{a}+{b}}{{a}},\frac{{a}+{b}−\mathrm{1}}{{a}},…….,\frac{{b}+\mathrm{1}}{{a}};\frac{{x}}{{a}^{{a}} }\right) \\ $$$$=\underset{{k}\geqslant\mathrm{0}} {\sum}\frac{{k}!}{\underset{{j}=\mathrm{0}}…

Prove-by-mathematcal-induction-that-1-1-1-2-1-1-2-3-1-1-2-3-n-2n-n-1-

Question Number 15671 by tawa tawa last updated on 12/Jun/17 $$\mathrm{Prove}\:\mathrm{by}\:\mathrm{mathematcal}\:\mathrm{induction}\:\mathrm{that} \\ $$$$\mathrm{1}\:+\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{2}}\:+\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{2}\:+\:\mathrm{3}}\:+\:…\:+\:\frac{\mathrm{1}}{\mathrm{1}\:+\:\mathrm{2}\:+\:\mathrm{3}\:+\:…\:\mathrm{n}}\:=\:\frac{\mathrm{2n}}{\mathrm{n}\:+\:\mathrm{1}} \\ $$ Answered by icyfalcon999 last updated on 12/Jun/17 $$\left.\mathrm{1}\right)\mathrm{proving}\:\mathrm{that}\:\mathrm{the}\:\mathrm{statement}\:\mathrm{true}\:\mathrm{when}\:\mathrm{n}=\mathrm{1} \\ $$$$\mathrm{R}.\mathrm{H}.\mathrm{S}.=\frac{\mathrm{2}\left(\mathrm{1}\right)}{\mathrm{1}+\mathrm{1}}=\frac{\mathrm{2}}{\mathrm{2}}=\mathrm{1}=\mathrm{L}.\mathrm{H}.\mathrm{S}.…

Question-146157

Question Number 146157 by henderson last updated on 11/Jul/21 Answered by gsk2684 last updated on 11/Jul/21 $$\underset{\frac{\mathrm{1}}{{e}}} {\overset{\lambda} {\int}}\frac{\mathrm{1}}{\mathrm{2}}\left(\mathrm{1}−\mathrm{ln}\:{x}\right)\frac{{d}\left(\mathrm{1}−\mathrm{ln}\:{x}\right)}{−\mathrm{1}} \\ $$$$−\frac{\mathrm{1}}{\mathrm{2}}\left[\frac{\left(\mathrm{1}−\mathrm{ln}\:{x}\right)^{\mathrm{2}} }{\mathrm{2}}\right]_{\frac{\mathrm{1}}{{e}}} ^{\lambda} \\ $$$$−\frac{\mathrm{1}}{\mathrm{4}}\left[\left(\mathrm{1}−\mathrm{ln}\:\lambda\right)^{\mathrm{2}}…

2-k-1-3-k-2-0-mod-k-5-min-k-k-N-

Question Number 146130 by Huy last updated on 11/Jul/21 $$\:\:\left(\mathrm{2}^{\mathrm{k}} +\mathrm{1}\right)\left(\mathrm{3}^{\mathrm{k}} +\mathrm{2}\right)\equiv\mathrm{0}\left(\mathrm{mod}\:\mathrm{k}+\mathrm{5}\right) \\ $$$$\:\mathrm{min}\:\mathrm{k}=?\:\:\:\left(\mathrm{k}\in\mathbb{N}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

n-0-1-81-n-3n-3-

Question Number 145982 by ArielVyny last updated on 10/Jul/21 $$\underset{{n}\geqslant\mathrm{0}} {\sum}\left(−\frac{\mathrm{1}}{\mathrm{81}}\right)^{{n}} \Gamma\left(\mathrm{3}{n}+\mathrm{3}\right)=?? \\ $$ Answered by Olaf_Thorendsen last updated on 10/Jul/21 $$\mathrm{diverges} \\ $$ Terms…