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Question Number 138989 by metamorfose last updated on 20/Apr/21 $${find}\:{the}\:{integers}\:{x}\:,\:{y}\:,\:{z}\:,\:{n}\:{that} \\ $$$${satisfy}\::\:\mathrm{2}^{{n}} ={x}!+{y}!+{z}! \\ $$ Answered by mindispower last updated on 21/Apr/21 $${let}\:{m}={min}\left({x},{y},{z}\right),{if}\:{m}\geqslant\mathrm{3}\Rightarrow \\ $$$${x}!+{y}!+{z}!\equiv\mathrm{0}\left[\mathrm{3}\right]\Leftrightarrow\mathrm{2}^{{n}}…
Question Number 7881 by Rasheed Soomro last updated on 23/Sep/16 $${A}\:{gets}\:\mathrm{1}/\mathrm{5}\:\:{of}\:\:{some}\:\:{amount}, \\ $$$${B}\:\:{gets}\:\mathrm{1}/\mathrm{3}\:\:{of}\:\:{remaining},\:{C} \\ $$$${gets}\:\mathrm{1}/\mathrm{6}\:{of}\:{remaining},\:{D}\:{gets} \\ $$$$\mathrm{1}/\mathrm{7}\:\:{of}\:\:{remaining}\:\:{and}\:{E}\:{gets} \\ $$$${rest}\:{of}\:{amount}.\:{What}\:{fraction} \\ $$$${gets}\:{E}\:? \\ $$ Commented by…
Question Number 73340 by Raxreedoroid last updated on 10/Nov/19 $$\mathrm{Is}\:\mathrm{there}\:\mathrm{any}\:\mathrm{pi}/\mathrm{product}\:\mathrm{notation}\:\mathrm{rules} \\ $$$$\mathrm{I}\:\mathrm{discovered}\:\mathrm{some}\:\mathrm{such}\:\mathrm{as}: \\ $$$$\underset{{k}={a}} {\overset{{b}} {\prod}}\left[{k}\right]=\frac{{b}!}{\left({a}−\mathrm{1}\right)!} \\ $$$$\underset{{k}={a}} {\overset{{b}} {\prod}}\left[{c}\right]={c}^{{b}−{a}+\mathrm{1}} \\ $$$$\underset{{k}={a}} {\overset{{b}} {\prod}}\left[{c}\centerdot{k}\right]=\underset{{k}={a}} {\overset{{b}}…
Question Number 7771 by FilupSmith last updated on 14/Sep/16 $$\mathrm{Show}\:\mathrm{that}: \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{n}}{\left({n}+\mathrm{2}\right)!}=\mathrm{3}−{e} \\ $$ Commented by FilupSmith last updated on 14/Sep/16 $$\mathrm{Amazing}! \\…
Question Number 138842 by peter frank last updated on 18/Apr/21 $${Find}\:{the}\:{sum}\:{to}\:{infinity} \\ $$$$\mathrm{1}+\frac{\mathrm{3}{x}}{\mathrm{1}!}+\frac{\mathrm{5}{x}^{\mathrm{2}} }{\mathrm{2}!}+\frac{\mathrm{7}{x}^{\mathrm{3}} }{\mathrm{3}!}+.. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 7750 by Tawakalitu. last updated on 13/Sep/16 $${Let}\:{n}\:=\:\left(\mathrm{2}^{\mathrm{31}} \right)\:×\:\left(\mathrm{3}^{\mathrm{19}} \right)\:{how}\:{many}\:{positive}\:{integer} \\ $$$${divisors}\:{of}\:{n}^{\mathrm{2}} \:{are}\:{less}\:{than}\:{n}\:{but}\:{do}\:{not}\:{divide}\:{n} \\ $$ Commented by Yozzia last updated on 13/Sep/16 $${n}^{\mathrm{2}}…
Question Number 7743 by Tawakalitu. last updated on 13/Sep/16 $${All}\:{the}\:{terms}\:{of}\:{the}\:{arithmetic}\:{progession}\: \\ $$$${u}_{\mathrm{1}} ,\:{u}_{\mathrm{2}} ,\:{u}_{\mathrm{3}} ,\:…\:{u}_{{n}} \:\:{are}\:{positive}\:.\:{use}\:{induction}\:{to} \\ $$$${prove}\:{that}\:{for}\:{n}\:\geqslant\:\mathrm{2} \\ $$$$\frac{\mathrm{1}}{{u}_{\mathrm{1}} {u}_{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{{u}_{\mathrm{2}} {u}_{\mathrm{3}} }\:+\:\frac{\mathrm{1}}{{u}_{\mathrm{3}} {u}_{\mathrm{4}}…
Question Number 138789 by 676597498 last updated on 18/Apr/21 Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 7723 by FilupSmith last updated on 12/Sep/16 $${p}_{{n}} ={n}\mathrm{th}\:\mathrm{prime}\:\:\left({p}_{\mathrm{1}} =\mathrm{2},\:\:{p}_{\mathrm{2}} =\mathrm{3},\:\:\:{p}_{\mathrm{3}} =\mathrm{5},\:…\right) \\ $$$$\mathrm{Do}\:\mathrm{the}\:\mathrm{following}\:\mathrm{sums}\:\mathrm{converge}?\:\mathrm{Prove}/\mathrm{disprove}. \\ $$$$\left(\mathrm{1}\right)\:\:\:\:\:\:\:\:{S}=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{n}}{{p}_{{n}} } \\ $$$$\left(\mathrm{2}\right)\:\:\:\:\:\:\:\:{S}=\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{n}}{{p}_{{n}}…