Category: Number Theory

Question Number 12861 by Gauri last updated on 04/May/17 $$change0.35\stackrel{-}{6}intop/qform$$$$$$ Answered by mrW1 last updated on 04/May/17 $${x}=\mathrm{0}.\mathrm{35}\bar {\mathrm{6}}=\mathrm{0}.\mathrm{356666666}…… \…

Question Number 12794 by tawa last updated on 01/May/17 $$\mathrm{Let}\mathrm{R}\mathrm{be}\mathrm{a}\mathrm{cummutative}\mathrm{ring}\mathrm{with}1,\mathrm{and}\mathrm{a},\mathrm{b}\in \mathrm{R}.\mathrm{suppose}\mathrm{a}\mathrm{is}\mathrm{ivertible}\mathrm{and}$$$$\mathrm{b}\mathrm{is}\mathrm{nilpotent}.\mathrm{Show}\mathrm{that}\mathrm{a}+\mathrm{b}\mathrm{is}\mathrm{ivertible}.$$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question Number 12330 by malwaan last updated on 22/Apr/17 $$\mathrm{find}\mathrm{the}\mathrm{fifth}\mathrm{digit}\mathrm{from}\mathrm{the}\mathrm{end}$$$$\mathrm{of}\mathrm{the}\mathrm{number}$$$$5^{5^{5^{4^5}}}$$ Terms of Service Privacy Policy Contact:…

Question Number 12106 by tawa last updated on 13/Apr/17 Answered by FilupS last updated on 13/Apr/17 $$\mathrm{\Sigma }{a}_n\mathrm{diverges}\mathrm{if}:\underset{n\to \mathrm{\infty }}{\lim }{a}_n\ne 0$$$$\mathrm{\Sigma }{ca}_n=c\mathrm{\Sigma }{a}_n$$$$\therefore{c}\Sigma{a}_{{n}}…

Question Number 11854 by tawa last updated on 02/Apr/17 $$\mathrm{Solve}\mathrm{by}\mathrm{mathematical}\mathrm{induction}\mathrm{that}$$$$1+\frac{1}{1+2}+\frac{1}{1+2+3}+\dots +\frac{1}{1+2+3+\dots +\mathrm{n}}=\frac{2\mathrm{n}}{\mathrm{n}+1}$$ Answered by sandy_suhendra last updated on 03/Apr/17 $$\mathrm{for}\mathrm{n}=1$$$$\mathrm{1}=\frac{\mathrm{2}.\mathrm{1}}{\mathrm{1}+\mathrm{1}}\:\left(\mathrm{is}\:\mathrm{true}\right) \…