Question Number 86088 by Serlea last updated on 27/Mar/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{series}\:\mathrm{below}: \\ $$$$\mathrm{1}+\mathrm{2}+\mathrm{3}−\mathrm{4}−\mathrm{5}−\mathrm{6}+\mathrm{7}+\mathrm{8}+\mathrm{9}−\mathrm{10}−\mathrm{11}−\mathrm{12}+\mathrm{13}+\mathrm{14}+\mathrm{15}…−\mathrm{3020} \\ $$ Commented by Kunal12588 last updated on 27/Mar/20 $${did}\:{yoy}\:{forgot}\:\mathrm{10}? \\ $$$${I}\:{think}\:{series}\:{should}\:{be}\:{like} \\…
Question Number 20523 by Tinkutara last updated on 27/Aug/17 $$\mathrm{Let}\:\mathrm{the}\:\mathrm{sum}\:\underset{{n}=\mathrm{1}} {\overset{\mathrm{9}} {\sum}}\frac{\mathrm{1}}{{n}\left({n}\:+\:\mathrm{1}\right)\left({n}\:+\:\mathrm{2}\right)}\:\mathrm{written} \\ $$$$\mathrm{in}\:\mathrm{its}\:\mathrm{lowest}\:\mathrm{terms}\:\mathrm{be}\:\frac{{p}}{{q}}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value} \\ $$$$\mathrm{of}\:{q}\:−\:{p}. \\ $$ Answered by ajfour last updated on 27/Aug/17…
Question Number 151587 by peter frank last updated on 22/Aug/21 $$\int\mathrm{sin}^{−\mathrm{1}} \sqrt{\frac{\mathrm{x}}{\mathrm{a}+\mathrm{x}}}\:\mathrm{dx} \\ $$ Answered by MJS_new last updated on 22/Aug/21 $${u}'=\mathrm{1}\:\rightarrow\:{u}={x} \\ $$$${v}=\mathrm{arcsin}\:\sqrt{\frac{{x}}{{x}+{a}}}\:\rightarrow\:{v}'=\frac{\sqrt{{a}}}{\mathrm{2}\left({x}+{a}\right)\sqrt{{x}}} \\…
Question Number 151585 by peter frank last updated on 22/Aug/21 $$\int\frac{\mathrm{dx}}{\mathrm{x}\sqrt{\mathrm{a}^{\mathrm{n}} +\mathrm{x}^{\mathrm{n}} }} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 151586 by peter frank last updated on 22/Aug/21 $$\int\mathrm{e}^{\mathrm{tan}^{−\mathrm{1}} \mathrm{x}} \left(\frac{\mathrm{1}+\mathrm{x}+\mathrm{x}^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} +\mathrm{1}}\right)\mathrm{dx} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 85857 by M±th+et£s last updated on 25/Mar/20 Answered by mind is power last updated on 26/Mar/20 $$\left.{n}^{\mathrm{2}} =\frac{\mathrm{1}}{\mathrm{4}}\left(\left(\mathrm{2}{n}−\mathrm{1}\right)^{\mathrm{2}} +\mathrm{2}\left(\mathrm{2}{n}−\mathrm{1}\right)+\mathrm{1}\right)\right) \\ $$$$\underset{{n}=\mathrm{1}} {\overset{+\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}−\mathrm{1}}…
Question Number 85832 by jagoll last updated on 25/Mar/20 $$\left(\mathrm{x}+\mathrm{x}^{−\mathrm{1}} \right)^{\mathrm{2}} +\left(\mathrm{x}^{\mathrm{2}} +\mathrm{x}^{−\mathrm{2}} \right)^{\mathrm{2}} +\left(\mathrm{x}^{\mathrm{3}} +\mathrm{x}^{−\mathrm{3}} \right)^{\mathrm{2}} \\ $$$$+\:…\:+\:\left(\mathrm{x}^{\mathrm{10}} +\mathrm{x}^{−\mathrm{10}} \right)^{\mathrm{2}} \:=\: \\ $$ Commented…
Question Number 20235 by naziri1920@gmail.com last updated on 24/Aug/17 $$ \\ $$$${if}\:\:\:\:\:\:\:\:{t}_{\left({m}+\mathrm{1}\right)} =\mathrm{2}{t}_{\left({n}+\mathrm{1}\right)} \\ $$$${so}\:{proof} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{t}_{\left(\mathrm{3}{m}+\mathrm{1}\right)} =\mathrm{2}{t}_{\left({m}+{n}+\mathrm{1}\right)\:\:\:\:\:\:} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{help}\:{please}……… \\ $$$$ \\ $$$$ \\…
Question Number 20217 by tawa tawa last updated on 24/Aug/17 Commented by tawa tawa last updated on 24/Aug/17 $$\mathrm{Please}\:\mathrm{help} \\ $$ Terms of Service Privacy…
Question Number 151256 by pticantor last updated on 19/Aug/21 $$\:{A}_{{n}} =\mathrm{2}^{{n}} +\mathrm{3}^{{n}} +\mathrm{4}^{{n}} +\mathrm{5}^{{n}} \\ $$$${B}_{{n}} =\mathrm{100}^{{n}} +\mathrm{101}^{{n}} +\mathrm{102}^{{n}} +\mathrm{103}^{{n}} \\ $$$$\left.\mathrm{1}\right)\boldsymbol{{find}}\:\boldsymbol{{values}}\:\boldsymbol{{of}}\:\boldsymbol{{n}}\:\boldsymbol{{while}}\:\mathrm{7}\mid\boldsymbol{{A}}_{\boldsymbol{{n}}} \\ $$$$\left.\mathrm{2}\right)\:\boldsymbol{{show}}\:\boldsymbol{{that}}\:\boldsymbol{{B}}_{\boldsymbol{{n}}} \equiv\boldsymbol{{A}}_{\boldsymbol{{n}}}…