Question Number 19637 by Tinkutara last updated on 13/Aug/17 $$\mathrm{Determine}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{five}-\mathrm{digit} \\ $$$$\mathrm{integers}\:\left(\mathrm{37}{abc}\right)\:\mathrm{in}\:\mathrm{base}\:\mathrm{10}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{each}\:\mathrm{of}\:\mathrm{the}\:\mathrm{numbers}\:\left(\mathrm{37}{abc}\right),\:\left(\mathrm{37}{bca}\right) \\ $$$$\mathrm{and}\:\mathrm{37}{cab}\:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{37}. \\ $$ Answered by Rasheed.Sindhi last updated on 14/Aug/17…
Question Number 84982 by M±th+et£s last updated on 18/Mar/20 $$\underset{{n}=\mathrm{2}} {\overset{\infty} {\sum}}\frac{{H}_{{n}} \:{H}_{{n}+\mathrm{1}} }{{n}^{\mathrm{3}} −{n}} \\ $$ Answered by Kamel Kamel last updated on 18/Mar/20…
Question Number 84976 by jagoll last updated on 18/Mar/20 Commented by jagoll last updated on 18/Mar/20 $$\mathrm{find}\:\mathrm{the}\:\mathrm{area}\: \\ $$ Commented by jagoll last updated on…
Question Number 150500 by EnterUsername last updated on 13/Aug/21 $$\mathrm{Find}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{first}-\mathrm{n}\:\mathrm{terms}\:\mathrm{in} \\ $$$${u}_{{n}} =\mathrm{4},\:\mathrm{9},\:\mathrm{15},\:\mathrm{23},\:\mathrm{35},\:\mathrm{55},\:\mathrm{91},\:\mathrm{159},… \\ $$ Commented by CAIMAN last updated on 13/Aug/21 Un=2^n-1+4n -1 Answered by…
Question Number 150462 by Tawa11 last updated on 12/Aug/21 Answered by puissant last updated on 12/Aug/21 $$\mathrm{I}=\underset{\mathrm{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{\mathrm{n}} \mathrm{ln}\left(\frac{\mathrm{2}+\mathrm{3n}}{\mathrm{1}+\mathrm{3n}}\right) \\ $$$$\mathrm{posons}\:\mathrm{U}_{\mathrm{n}} =\left(−\mathrm{1}\right)^{\mathrm{n}} \mathrm{ln}\left(\frac{\mathrm{2}+\mathrm{3n}}{\mathrm{1}+\mathrm{3n}}\right) \\…
Question Number 84904 by john santu last updated on 17/Mar/20 $$\mathrm{3}^{\mathrm{2x}^{\mathrm{2}} } \:+\:\mathrm{3}^{\mathrm{x}^{\mathrm{2}} +\mathrm{2x}+\mathrm{5}} \:\geqslant\:\mathrm{10}.\:\mathrm{3}^{\mathrm{4x}+\mathrm{6}} \\ $$$$ \\ $$ Commented by john santu last updated…
Question Number 19330 by Tinkutara last updated on 09/Aug/17 $$\mathrm{A}\:\mathrm{triangle}\:\mathrm{with}\:\mathrm{perimeter}\:\mathrm{7}\:\mathrm{has}\:\mathrm{integer} \\ $$$$\mathrm{side}\:\mathrm{lengths}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{maximum} \\ $$$$\mathrm{possible}\:\mathrm{area}\:\mathrm{of}\:\mathrm{such}\:\mathrm{a}\:\mathrm{triangle}? \\ $$ Answered by mrW1 last updated on 09/Aug/17 $$\mathrm{3}/\mathrm{3}/\mathrm{1}\Rightarrow\mathrm{A}=\sqrt{\mathrm{3}.\mathrm{5}×\mathrm{0}.\mathrm{5}×\mathrm{0}.\mathrm{5}×\mathrm{2}.\mathrm{5}}=\mathrm{1}.\mathrm{479} \\…
Question Number 19182 by Tinkutara last updated on 06/Aug/17 $$\mathrm{Find}\:\mathrm{all}\:\mathrm{three}\:\mathrm{digit}\:\mathrm{numbers}\:{abc}\:\left(\mathrm{with}\right. \\ $$$$\left.\mathrm{a}\:\neq\:\mathrm{0}\right)\:\mathrm{such}\:\mathrm{that}\:\mathrm{a}^{\mathrm{2}} \:+\:\mathrm{b}^{\mathrm{2}} \:+\:\mathrm{c}^{\mathrm{2}} ,\:\mathrm{is}\:\mathrm{divisible} \\ $$$$\mathrm{by}\:\mathrm{26}. \\ $$ Answered by RasheedSindhi last updated on…
Question Number 84677 by jagoll last updated on 15/Mar/20 $$\underset{\mathrm{k}\:=\:\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{k}^{\mathrm{2}} }{\mathrm{2}^{\mathrm{k}} }\:?\: \\ $$ Commented by Tony Lin last updated on 15/Mar/20 $$\frac{\mathrm{1}}{\mathrm{1}−{x}}=\mathrm{1}+{x}+{x}^{\mathrm{2}}…
Question Number 19064 by 99 last updated on 03/Aug/17 Commented by 99 last updated on 03/Aug/17 $${sir}\:{please}\:{solve}\:{this}\:{question} \\ $$ Commented by 99 last updated on…