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Question Number 140462 by ZiYangLee last updated on 08/May/21 Commented by mr W last updated on 08/May/21 $$T_n={ar}^{n-1}$$$$\frac{{T}_{{n}+\mathrm{4}} −{T}_{{n}+\mathrm{2}} }{{T}_{{n}+\mathrm{1}} }=\frac{{ar}^{{n}+\mathrm{3}} −{ar}^{{n}+\mathrm{1}}…

Question Number 9372 by geovane10math last updated on 03/Dec/16 $$\mathrm{I}\mathrm{was}\mathrm{able}\mathrm{to}\mathrm{discover}\mathrm{the}\mathrm{conditions}\mathrm{for}$$$$\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{two}\mathrm{irrational}\mathrm{numbers}\mathrm{be}\mathrm{an}$$$$\mathrm{integer}\mathrm{and}\mathrm{the}\mathrm{conditions}\mathrm{for}\mathrm{the}\mathrm{sum}$$$$\mathrm{be}\mathrm{a}\mathrm{finite}\mathrm{decimal}.$$$$\mathrm{But}\mathrm{I}\mathrm{can}\mathrm{not}\mathrm{do}\mathrm{the}\mathrm{same}\mathrm{for}\mathrm{periodic}$$$$\mathrm{tithe}.$$$$\mathrm{Someone}\mathrm{can}\mathrm{help}\mathrm{me},\mathrm{please}?$$$$ \…

Question Number 74863 by mrS last updated on 02/Dec/19 Commented by abdomathmax last updated on 03/Dec/19 $${we}\:{have}\:{S}=\sum_{{n}=\mathrm{1}} ^{\mathrm{45}} \:\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\:=\sum_{{p}=\mathrm{1}} ^{\left[\frac{\mathrm{45}}{\mathrm{2}}\right]} \:\:\frac{\mathrm{1}}{\left(\mathrm{2}{p}\right)^{\mathrm{2}} }\:+\sum_{{p}=\mathrm{0}} ^{\left[\frac{\mathrm{45}−\mathrm{1}}{\mathrm{2}}\right]} \:\frac{\mathrm{1}}{\left(\mathrm{2}{p}+\mathrm{1}\right)^{\mathrm{2}}…

Question Number 140384 by Willson last updated on 07/May/21 Answered by benjo_mathlover last updated on 07/May/21 $$\left(2\right)\underset{x\to 0}{\lim }\frac{{({\mathrm{x}}^{\mathrm{p}}+1)}^{\mathrm{n}}{({\mathrm{x}}^{\mathrm{q}}+1)}^{\mathrm{m}}-1}{\mathrm{x}}=$$$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{1}+\mathrm{nx}^{\mathrm{p}}…

Question Number 140367 by aliibrahim1 last updated on 06/May/21 Answered by meetbhavsar25 last updated on 06/May/21 $$Answeris\frac{9}{25}.$$$$x^{2}hasminimumvalue0.$$$$y^{2}hasminimumvalue0.$$$$\left({z}−\mathrm{1}\right)^{\mathrm{2}}…