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Author: Tinku Tara

Given-a-b-and-c-are-real-numbers-and-a-lt-b-lt-c-If-1-a-1-b-1-c-1-18-find-minimum-value-of-a-

Question Number 134069 by john_santu last updated on 27/Feb/21 $${Given}\:{a},{b}\:{and}\:{c}\:{are}\:{real}\:{numbers}\:{and}\:{a}<{b}<{c}. \\ $$$${If}\:\frac{\mathrm{1}}{{a}}\:+\:\frac{\mathrm{1}}{{b}}\:+\:\frac{\mathrm{1}}{{c}}\:=\:\frac{\mathrm{1}}{\mathrm{18}}\:,\:{find}\:{minimum}\:{value}\:{of}\:{a}. \\ $$ Commented by mr W last updated on 27/Feb/21 $${no}\:{minimum}\:{for}\:{a}\:{exists}. \\ $$…

Question-134064

Question Number 134064 by mr W last updated on 27/Feb/21 Commented by mr W last updated on 27/Feb/21 $${find}\:{the}\:{angle}\:\theta\:{at}\:{which}\:{the}\:{falling} \\ $$$${rod}\:{begins}\:{to}\:{slip}\:{on}\:{the}\:{ground}\:{if} \\ $$$${the}\:{friction}\:{coefficient}\:{between}\:{rod} \\ $$$${and}\:{ground}\:{is}\:\mu.…

Calculate-lim-n-k-2-n-k-3-1-k-3-1-

Question Number 134067 by bramlexs22 last updated on 27/Feb/21 $$\:\mathrm{Calculate}\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\underset{\mathrm{k}=\mathrm{2}} {\overset{\mathrm{n}} {\prod}}\:\frac{\mathrm{k}^{\mathrm{3}} −\mathrm{1}}{\mathrm{k}^{\mathrm{3}} +\mathrm{1}}\:=\:? \\ $$ Answered by john_santu last updated on 27/Feb/21 $$\:{since}\:\frac{{k}^{\mathrm{3}}…

If-a-n-is-a-convergent-series-of-nonnegative-terms-what-can-be-said-about-a-n-a-n-1-a-always-converges-b-always-diverges-c-may-converges-or-diverge-

Question Number 134061 by benjo_mathlover last updated on 27/Feb/21 $$\mathrm{If}\:\Sigma\:\mathrm{a}_{\mathrm{n}} \:\mathrm{is}\:\mathrm{a}\:\mathrm{convergent}\:\mathrm{series}\:\mathrm{of} \\ $$$$\mathrm{nonnegative}\:\mathrm{terms},\mathrm{what}\:\mathrm{can}\:\mathrm{be} \\ $$$$\mathrm{said}\:\mathrm{about}\:\Sigma\:\mathrm{a}_{\mathrm{n}} .\mathrm{a}_{\mathrm{n}+\mathrm{1}} \:? \\ $$$$\left(\mathrm{a}\right)\:\mathrm{always}\:\mathrm{converges} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{always}\:\mathrm{diverges} \\ $$$$\left(\mathrm{c}\right)\:\mathrm{may}\:\mathrm{converges}\:\mathrm{or}\:\mathrm{diverge} \\ $$…

If-p-gt-1-and-q-gt-1-what-can-be-said-about-the-convergence-of-n-2-1-n-p-ln-n-q-a-always-converges-b-always-diverges-c-may-converges-or-diverges-

Question Number 134060 by benjo_mathlover last updated on 27/Feb/21 $$\mathrm{If}\:\mathrm{p}>\mathrm{1}\:\mathrm{and}\:\mathrm{q}>\mathrm{1}\:\mathrm{what}\:\mathrm{can}\:\mathrm{be} \\ $$$$\mathrm{said}\:\mathrm{about}\:\mathrm{the}\:\mathrm{convergence}\: \\ $$$$\mathrm{of}\:\underset{\mathrm{n}=\mathrm{2}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{p}} .\left(\mathrm{ln}\:\mathrm{n}\right)^{\mathrm{q}} }\:? \\ $$$$\left(\mathrm{a}\right)\:\mathrm{always}\:\mathrm{converges} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{always}\:\mathrm{diverges} \\ $$$$\left(\mathrm{c}\right)\:\mathrm{may}\:\mathrm{converges}\:\mathrm{or}\:\mathrm{diverges} \\…