Question Number 7831 by Chantria last updated on 18/Sep/16 Commented by prakash jain last updated on 18/Sep/16 $${S}_{{n}} =\frac{{n}+\mathrm{2}}{{n}!}+\frac{\mathrm{2}}{{k}!}+\frac{\mathrm{7}}{{k}!}+….+\frac{{n}^{\mathrm{2}} −\mathrm{2}}{{k}!}=\frac{{n}+\mathrm{2}}{{n}!}+\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{{k}^{\mathrm{2}} −\mathrm{2}}{{k}!} \\ $$$${n}^{\mathrm{2}}…
Question Number 7827 by 314159 last updated on 17/Sep/16 Commented by Yozzia last updated on 18/Sep/16 $$\bigtriangleup{ABC}\:{is}\:{isosceles}\:{with}\:{b}={c}. \\ $$$${a}\leqslant{b}+{c}=\mathrm{2}{b}=\mathrm{2}{c}\:\:\left({Triangle}\:{inequality}\right) \\ $$$${I}'{ve}\:{gotten}\:{that}\:{far}\:{in}\:{the}\:{problem}. \\ $$ Terms of…
Question Number 138897 by tabata last updated on 19/Apr/21 Commented by tabata last updated on 19/Apr/21 $${prove}\:{this} \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 138899 by mohammad17 last updated on 19/Apr/21 $$\int{cos}\left({ln}\left({sinx}\right)\right){dx} \\ $$ Answered by Ar Brandon last updated on 19/Apr/21 $$\mathrm{Let}\:\mathrm{u}=\mathrm{sinx} \\ $$ Terms of…
Question Number 7788 by Chantria last updated on 15/Sep/16 $$\left({a}_{{n}} \right)_{{n}\in{N}} \:{such}\:{that}\:{a}_{\mathrm{1}} =\frac{\mathrm{1}}{\mathrm{2}}\: \\ $$$${and}\:{a}_{{n}+\mathrm{1}} =\frac{{a}_{{n}} ^{\mathrm{2}} }{{a}_{{n}} ^{\mathrm{2}} −{a}_{{n}} +\mathrm{1}} \\ $$$${Prove}\:{that}\:{a}_{\mathrm{1}} +{a}_{\mathrm{2}} +{a}_{\mathrm{3}}…
Question Number 7782 by Chantria last updated on 15/Sep/16 $$\:{Given}\:{a},{b},{c}\:\in{N}\:;\:{prove}\:{that} \\ $$$$\:\frac{\mathrm{1}+{a}}{\mathrm{1}+\mathrm{2}{a}}\:+\:\frac{\mathrm{1}+{b}}{\mathrm{1}+\mathrm{2}{b}}\:+\:\frac{\mathrm{1}+{c}}{\mathrm{1}+\mathrm{2}{c}}\:\leqslant\:\mathrm{2} \\ $$ Commented by sou1618 last updated on 15/Sep/16 $${Let}\:{f}\left({n}\right)=\frac{\mathrm{1}+{n}}{\mathrm{1}+\mathrm{2}{n}}\:\:\left({n}\geqslant\mathrm{1}\right) \\ $$$$ \\…
Question Number 7785 by B last updated on 15/Sep/16 $${x}^{\mathrm{2}} −{x}^{\mathrm{2}} ={x}^{\mathrm{2}} −{x}^{\mathrm{2}} \\ $$$$\left({x}−{x}\right)\left({x}+{x}\right)={x}\left({x}−{x}\right) \\ $$$${x}−{x}={x} \\ $$$$\mathrm{2}{x}={x} \\ $$$$\mathrm{2}=\mathrm{1} \\ $$ Commented by…
Question Number 7781 by 314159 last updated on 15/Sep/16 Commented by prakash jain last updated on 15/Sep/16 $${f}\left(\mathrm{1}\right)=\mathrm{2} \\ $$$${f}\left(\mathrm{2}\right)=\mathrm{8} \\ $$$${f}\left({x}+{y}\right)−{kxy}={f}\left({x}\right)+\mathrm{2}{y}^{\mathrm{2}} \\ $$$${x}=\mathrm{0} \\…
Question Number 7775 by sandy_suhendra last updated on 14/Sep/16 Commented by sou1618 last updated on 15/Sep/16 $${x}=\mathrm{4}−\sqrt{\mathrm{3}} \\ $$$${x}^{\mathrm{4}} −\mathrm{6}{x}^{\mathrm{3}} −\mathrm{2}{x}^{\mathrm{2}} +\mathrm{18}{x}+\mathrm{23}=? \\ $$$$ \\…
Question Number 7766 by 314159 last updated on 14/Sep/16 Commented by sou1618 last updated on 14/Sep/16 $${f}\left({xy}\right)={f}\left({x}\right)+{f}\left({y}\right) \\ $$$${f}\left({e}^{\mathrm{2}} \right)=−\mathrm{8}\:\:\:\:\:\:\:\left({Q}\mathrm{7771}\right) \\ $$$$ \\ $$$${f}''\left(\mathrm{2}\right)=?? \\…