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If-f-t-2-e-t-1-a-Does-f-t-exists-for-all-n-b-If-it-exist-does-it-converge-c-If-the-sequence-converge-does-the-limit-converge-d-Is-the-solution-uniques-

Question Number 192544 by Mastermind last updated on 20/May/23 $$\mathrm{If}\:\mathrm{f}\left(\mathrm{t}\right)\:=\:\mathrm{2}\left(\mathrm{e}^{\mathrm{t}} \:−\:\mathrm{1}\right) \\ $$$$\left.\mathrm{a}\right)\:\mathrm{Does}\:\mathrm{f}\left(\mathrm{t}\right)\:\mathrm{exists}\:\mathrm{for}\:\mathrm{all}\:\mathrm{n}\:? \\ $$$$\left.\mathrm{b}\right)\:\mathrm{If}\:\mathrm{it}\:\mathrm{exist},\:\mathrm{does}\:\mathrm{it}\:\mathrm{converge}\:? \\ $$$$\left.\mathrm{c}\right)\:\mathrm{If}\:\mathrm{the}\:\mathrm{sequence}\:\mathrm{converge},\:\mathrm{does}\:\mathrm{the} \\ $$$$\mathrm{limit}\:\mathrm{converge}\:? \\ $$$$\left.\mathrm{d}\right)\:\mathrm{Is}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{uniques}\:? \\ $$ Commented by…

n-1-n-7-7-n-

Question Number 126977 by Dwaipayan Shikari last updated on 25/Dec/20 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{n}^{\mathrm{7}} }{\mathrm{7}^{{n}} } \\ $$ Commented by MJS_new last updated on 25/Dec/20 $$=\frac{\mathrm{285929}}{\mathrm{11664}}…

A-heat-transfer-of-9-0-10-5-J-is-required-to-convert-a-block-of-ice-at-20-C-to-water-at-15-C-what-was-the-mass-of-the-block-of-ice-

Question Number 192472 by Mastermind last updated on 19/May/23 $$\mathrm{A}\:\mathrm{heat}\:\mathrm{transfer}\:\mathrm{of}\:\mathrm{9}.\mathrm{0}×\mathrm{10}^{\mathrm{5}} \mathrm{J}\:\mathrm{is}\:\mathrm{required} \\ $$$$\mathrm{to}\:\mathrm{convert}\:\mathrm{a}\:\mathrm{block}\:\mathrm{of}\:\mathrm{ice}\:\mathrm{at}\:\mathrm{20}°\mathrm{C}\:\mathrm{to} \\ $$$$\mathrm{water}\:\mathrm{at}\:\mathrm{15}°\mathrm{C},\:\mathrm{what}\:\mathrm{was}\:\mathrm{the}\:\mathrm{mass}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{block}\:\mathrm{of}\:\mathrm{ice}\:? \\ $$ Answered by MikeH last updated on…

1-1-1-2-3-2-2-5-3-2-7-4-2-9-

Question Number 126934 by Dwaipayan Shikari last updated on 25/Dec/20 $$\frac{\mathrm{1}}{\mathrm{1}!}+\frac{\mathrm{1}!^{\mathrm{2}} }{\mathrm{3}!}+\frac{\mathrm{2}!^{\mathrm{2}} }{\mathrm{5}!}+\frac{\mathrm{3}!^{\mathrm{2}} }{\mathrm{7}!}+\frac{\mathrm{4}!^{\mathrm{2}} }{\mathrm{9}!}+…. \\ $$ Commented by Dwaipayan Shikari last updated on 25/Dec/20…

The-first-term-of-an-arithmetic-series-is-7-and-the-last-is-70-and-the-sum-is-385-find-the-number-of-terms-in-the-series-and-its-common-difference-

Question Number 192450 by Mastermind last updated on 18/May/23 $$\mathrm{The}\:\mathrm{first}\:\mathrm{term}\:\mathrm{of}\:\mathrm{an}\:\mathrm{arithmetic}\:\mathrm{series} \\ $$$$\mathrm{is}\:\mathrm{7}\:\mathrm{and}\:\mathrm{the}\:\mathrm{last}\:\mathrm{is}\:\mathrm{70}.\:\mathrm{and}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{is} \\ $$$$\mathrm{385}.\:\mathrm{find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{terms}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{series}\:\mathrm{and}\:\mathrm{its}\:\mathrm{common}\:\mathrm{difference}. \\ $$ Answered by AST last updated on 18/May/23…

The-sum-of-three-numbers-in-arith-metic-progression-is-18-and-sum-of-square-is-206-find-the-numbers-

Question Number 192444 by Mastermind last updated on 18/May/23 $$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{three}\:\mathrm{numbers}\:\mathrm{in}\:\mathrm{arith}- \\ $$$$\mathrm{metic}\:\mathrm{progression}\:\mathrm{is}\:\mathrm{18}\:\mathrm{and}\:\mathrm{sum}\:\mathrm{of} \\ $$$$\mathrm{square}\:\mathrm{is}\:\mathrm{206}.\:\mathrm{find}\:\mathrm{the}\:\mathrm{numbers} \\ $$ Commented by Tinku Tara last updated on 19/May/23 $$\mathrm{Automatic}\:\mathrm{tagging}\:\mathrm{may}\:\mathrm{sometime}…