Question Number 184939 by Mastermind last updated on 14/Jan/23 $$\mathrm{What}'\mathrm{s}\:\mathrm{the}\:\mathrm{convergent}\:\mathrm{equation} \\ $$$$\mathrm{of}\:\mathrm{this}\:\mathrm{series}? \\ $$$$\mathrm{x}_{\mathrm{1}} ^{\mathrm{2}} +\mathrm{x}_{\mathrm{2}} ^{\mathrm{2}} +\mathrm{x}_{\mathrm{3}} ^{\mathrm{2}} +…+\mathrm{x}_{\mathrm{n}} ^{\mathrm{2}} \\ $$$$ \\ $$$$\mathrm{Help}!…
Question Number 184918 by Mastermind last updated on 14/Jan/23 $$\mathrm{Show}\:\mathrm{that}\: \\ $$$$\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{5}}+\frac{\mathrm{1}}{\mathrm{6}}+…\:\mathrm{is}\: \\ $$$$\mathrm{not}\:\mathrm{convergent} \\ $$$$ \\ $$$$\mathrm{Hi} \\ $$ Commented by Frix last updated…
Question Number 184920 by Mastermind last updated on 13/Jan/23 $$\mathrm{Investigate}\:\mathrm{the}\:\mathrm{series} \\ $$$$\frac{\mathrm{1}}{\mathrm{1}×\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{2}×\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{3}×\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{4}×\mathrm{5}}+… \\ $$$$\mathrm{Does}\:\mathrm{it}\:\mathrm{Converges}\:\mathrm{or}\:\mathrm{Diverges}? \\ $$ Answered by aba last updated on 14/Jan/23 $$\mathrm{S}_{\mathrm{n}} =\underset{\mathrm{k}=\mathrm{1}}…
Question Number 184915 by Mastermind last updated on 13/Jan/23 $$\mathrm{Consider}\:\mathrm{the}\:\mathrm{series}\:\mathrm{below} \\ $$$$\mathrm{1}+\mathrm{5}+\mathrm{25}+\mathrm{125}+…\:\mathrm{Investigate} \\ $$$$\mathrm{whether}\:\mathrm{it}\:\mathrm{is}\:\mathrm{convergent}\:\mathrm{or}\: \\ $$$$\mathrm{divergent}. \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Thanks} \\ $$ Commented…
Question Number 119376 by Abdulmajeed last updated on 24/Oct/20 $${Solve}\:{for}\:\boldsymbol{{x}}\:{in}\:{the}\:{equation}\:{below} \\ $$$${ax}^{\mathrm{2}} \:+{bx}\:+\:{c}\:=\:\mathrm{0}. \\ $$ Commented by ZiYangLee last updated on 24/Oct/20 $${x}=\frac{−{b}\pm\sqrt{{b}^{\mathrm{2}} −\mathrm{4}{ac}}}{\mathrm{2}{a}} \\…
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Question Number 184873 by topgrace100 last updated on 13/Jan/23 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{real}\:\mathrm{number}\:\mathrm{satisfying} \\ $$$$\:\mathrm{x}=\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\mathrm{x}}}} \\ $$ Answered by Rasheed.Sindhi last updated on 13/Jan/23 $$\:\mathrm{x}=\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\mathrm{x}}}} \\ $$$$\:\mathrm{x}=\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+\sqrt{\mathrm{1}+…}}}}} \\…
Question Number 119316 by Dwaipayan Shikari last updated on 23/Oct/20 $$\frac{\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{n}^{{n}} }}{\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\left(−\mathrm{1}\right)^{{n}+\mathrm{1}} \frac{\mathrm{1}}{{n}^{{n}} }} \\ $$ Terms of Service Privacy Policy…
Question Number 184832 by Mastermind last updated on 12/Jan/23 $$\mathrm{Given}\:\mathrm{the}\:\mathrm{acceleration}\: \\ $$$$\mathrm{a}=−\mathrm{4sin2t},\:\mathrm{initial}\:\mathrm{velocity}\: \\ $$$$\mathrm{v}\left(\mathrm{0}\right)=\mathrm{2},\:\mathrm{and}\:\mathrm{the}\:\mathrm{initial}\:\mathrm{position}\: \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{body}\:\mathrm{as}\:\mathrm{s}\left(\mathrm{0}\right)=−\mathrm{3},\:\mathrm{find}\:\mathrm{the} \\ $$$$\mathrm{body}'\mathrm{s}\:\mathrm{position}\:\mathrm{at}\:\mathrm{time}\:\mathrm{t}. \\ $$$$ \\ $$$$\mathrm{Hi} \\ $$ Commented…
Question Number 53736 by Mikael_Marshall last updated on 25/Jan/19 $$\sqrt{\mathrm{32}+\mathrm{10}\sqrt{\mathrm{7}}}+\sqrt{\mathrm{32}−\mathrm{10}\sqrt{\mathrm{7}}}=? \\ $$ Commented by Kunal12588 last updated on 25/Jan/19 $${just}\:{want}\:{to}\:{add}\:{something} \\ $$$$\sqrt{{m}+\sqrt{{n}\:}}\:{getting}\:{square}\:{root}\:{of}\:{a}\:{surd} \\ $$$$\sqrt{{m}+\sqrt{{n}}}=\sqrt{{a}}+\sqrt{{b}} \\…