Question Number 7846 by Tinku Tara last updated on 20/Sep/16 $$\mathrm{There}\:\mathrm{is}\:\mathrm{new}\:\mathrm{update}\:\mathrm{available}. \\ $$$$\mathrm{The}\:\mathrm{following}\:\mathrm{enhacements}\:\mathrm{are}\:\mathrm{made}\:\mathrm{in} \\ $$$$\mathrm{this}\:\mathrm{update} \\ $$$$\bullet\:\mathrm{You}\:\mathrm{can}\:\mathrm{now}\:\mathrm{zoom}\:\mathrm{on}\:\mathrm{images}\:\mathrm{posted}\:\mathrm{on} \\ $$$$\:\:\:\:\mathrm{the}\:\mathrm{forum}. \\ $$$$\bullet\:\mathrm{Preview}\:\mathrm{of}\:\mathrm{the}\:\mathrm{image}\:\mathrm{is}\:\mathrm{available}\:\mathrm{while} \\ $$$$\:\:\:\:\mathrm{answering}\:\mathrm{or}\:\mathrm{commenting}.\:\mathrm{You}\:\mathrm{can} \\ $$$$\:\:\:\:\mathrm{zoom}\:\mathrm{within}\:\mathrm{the}\:\mathrm{preview}\:\mathrm{as}\:\mathrm{well}.…
Question Number 7840 by Chantria last updated on 19/Sep/16 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{first}\:\mathrm{digit}\:\mathrm{after}\:\mathrm{the} \\ $$$$\mathrm{decimal}\:\mathrm{point}\:\mathrm{of}\:\mathrm{the}\:\mathrm{number}\:\frac{\mathrm{1}}{\mathrm{1009}}+\frac{\mathrm{1}}{\mathrm{1010}}+…+\frac{\mathrm{1}}{\mathrm{2016}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
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} \\…