Question Number 6902 by Tawakalitu. last updated on 02/Aug/16 $$\mathrm{1}^{\mathrm{6}} \:+\:\mathrm{3}^{\mathrm{6}} \:+\:\mathrm{5}^{\mathrm{6}} \:+\:…\:+\:\left(\mathrm{2}{n}\:−\:\mathrm{1}\right)^{\mathrm{6}} \:\:=\:\:{B} \\ $$$$ \\ $$$${Solve}\:{for}\:{B}. \\ $$ Commented by Yozzii last updated…
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Question Number 6892 by Tawakalitu. last updated on 01/Aug/16 $$\mathrm{1}^{\mathrm{6}} \:+\:\mathrm{3}^{\mathrm{6}} \:+\:\mathrm{5}^{\mathrm{6}} \:+\:….\:+\:\left(\mathrm{2}{n}\:−\:\mathrm{1}\right)^{\mathrm{6}} \:\:=\:\:{B} \\ $$$$ \\ $$$${Find}\:{the}\:{value}\:{of}\:{B}\: \\ $$ Terms of Service Privacy Policy…
Question Number 6843 by Tawakalitu. last updated on 30/Jul/16 $$\mathrm{2}^{\mathrm{10}} \:+\:\mathrm{3}^{\mathrm{20}} \:+\:\mathrm{4}^{\mathrm{30}} \:+\:\mathrm{5}^{\mathrm{40}} \:+\:\mathrm{6}^{\mathrm{50}} \:\:\left({mod}\:\mathrm{7}\right)\:=\:? \\ $$ Commented by prakash jain last updated on 31/Jul/16…
Question Number 137907 by peter frank last updated on 08/Apr/21 Answered by EnterUsername last updated on 08/Apr/21 $$\int_{\mathrm{1}} ^{{e}} \frac{\mathrm{1}+{lnx}}{{x}}{dx}=\int_{\mathrm{1}} ^{{e}} \left(\frac{\mathrm{1}}{{x}}+\frac{{lnx}}{{x}}\right){dx} \\ $$$$=\left[{lnx}+\frac{{ln}^{\mathrm{2}} {x}}{\mathrm{2}}\right]_{\mathrm{1}}…
Question Number 6831 by Tawakalitu. last updated on 30/Jul/16 $${Find}\:{the}\:\mathrm{100}{th}\:{digits}\:{of}\:{this}\:{sum}\: \\ $$$$\mathrm{1}\:+\:\mathrm{50}\:+\:\mathrm{50}^{\mathrm{2}} \:+\:…..\:+\:\mathrm{50}^{\mathrm{999}} \\ $$ Commented by prakash jain last updated on 31/Jul/16 $$\mathrm{How}\:\mathrm{did}\:\mathrm{you}\:\mathrm{get} \\…
Question Number 6832 by Tawakalitu. last updated on 30/Jul/16 $${What}\:{remainder}\:{does}\:\mathrm{3}^{\mathrm{6}{n}} \:−\:\mathrm{2}^{\mathrm{6}{n}} \:\:{leave}\:{when}\:{divided}\:{by}\:\mathrm{35}\:{for}\: \\ $$$${any}\:{value}\:{of}\:{n}\: \\ $$ Commented by Yozzii last updated on 30/Jul/16 $$\mathrm{3}^{\mathrm{6}{n}} −\mathrm{2}^{\mathrm{6}{n}}…
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Question Number 137899 by bemath last updated on 08/Apr/21 $${Given}\:{the}\:{series}\: \\ $$$${a}_{{n}} =\:\mathrm{3}{a}_{{n}−\mathrm{1}} +\:\mathrm{2}{a}_{{n}−\mathrm{2}} \:{with}\: \\ $$$${a}_{\mathrm{1}} =\mathrm{11}\:\&\:{a}_{\mathrm{2}} \:=\:\mathrm{21}.\:{Find}\:{a}_{{n}} . \\ $$ Answered by benjo_mathlover…
Question Number 137875 by physicstutes last updated on 07/Apr/21 $$\mathrm{Proof}\:\mathrm{by}\:\mathrm{mathematical}\:\mathrm{induction}\:\mathrm{that}\: \\ $$$$\:{f}\left({n}\right)\:=\:{n}^{\mathrm{3}} \:+\:\mathrm{5}{n}\: \\ $$$$\mathrm{is}\:\mathrm{a}\:\mathrm{multiple}\:\mathrm{of}\:\mathrm{6}. \\ $$ Answered by mathmax by abdo last updated on…