Question Number 386 by 123456 last updated on 25/Jan/15 $${p}_{{n}+\mathrm{1}} ={p}_{{n}} +{q}_{{n}} \\ $$$${q}_{{n}+\mathrm{1}} ={p}_{{n}} {q}_{{n}} \\ $$$${p}_{\mathrm{0}} =\mathrm{2} \\ $$$${q}_{\mathrm{0}} =\mathrm{3} \\ $$$${f}\left({x}\right)=\frac{{p}_{\mathrm{0}} }{{q}_{\mathrm{0}}…
Question Number 65918 by mathmax by abdo last updated on 05/Aug/19 $${simplify}\:{A}_{{n}} =\left(\mathrm{2}+{i}\sqrt{\mathrm{5}}\right)^{{n}} \:+\left(\mathrm{2}−{i}\sqrt{\mathrm{5}}\right)^{{n}} \\ $$$${and}\:{B}_{{n}} =\left(\mathrm{2}+{i}\sqrt{\mathrm{5}}\right)^{{n}} −\left(\mathrm{2}−{i}\sqrt{\mathrm{5}}\right)^{{n}} \\ $$ Commented by mathmax by abdo…
Question Number 65916 by mathmax by abdo last updated on 05/Aug/19 $${solve}\:{inside}\:{N}\:{and}\:{Z}\:\:{the}\:{equation}\:\frac{\mathrm{1}}{{x}}+\frac{\mathrm{1}}{{y}}=\frac{\mathrm{1}}{\mathrm{15}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 65917 by mathmax by abdo last updated on 05/Aug/19 $${prove}\:{that}\:\mathrm{1}\:+\frac{\mathrm{1}}{\mathrm{2}}\:+\frac{\mathrm{1}}{\mathrm{3}}\:+…+\frac{\mathrm{1}}{{n}}\:=\frac{{p}_{{n}} }{\mathrm{2}{q}_{{n}} }\:\:{with}\:{p}_{{n}} {odd} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 377 by 123456 last updated on 25/Jan/15 $${f}_{{n}+\mathrm{1}} \left({x}\right)=\frac{{f}_{{n}} \left({x}\right)}{{n}+\mathrm{1}}+{n} \\ $$$${f}_{\mathrm{0}} \left({x}\right)=\mathrm{1} \\ $$$${f}_{\mathrm{5}} \left({x}\right)=? \\ $$ Answered by prakash jain last…
Question Number 65915 by mathmax by abdo last updated on 05/Aug/19 $${let}\:{p}\:{prime}\:{not}\:\mathrm{0}\:\:{and}\:{n}\:{integr}\:/\mathrm{1}\leqslant{n}<{p}\:{prove}\:{that} \\ $$$$\frac{\left({p}−\mathrm{1}\right)\left({p}−\mathrm{2}\right)….\left({p}−{n}\right)}{{n}!}\:−\left(−\mathrm{1}\right)^{{n}} \:\:{is}\:{integr}\:{and}\:{divided}\:{by}\:{p} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 359 by 123456 last updated on 25/Jan/15 $${f}_{{n}} \left({x}\right)=\mathrm{1}+{c}_{\mathrm{0}} \left({n}\right){x}+{c}_{\mathrm{1}} \left({n}\right){x}^{\mathrm{2}} +{c}_{\mathrm{2}} \left({n}\right){x}^{\mathrm{3}} \\ $$$${c}_{{n}} \left({x}\right)={x}\left({x}−\mathrm{1}\right)\left({x}−\mathrm{2}\right)\centerdot\centerdot\centerdot\left({x}−{n}\right) \\ $$$${n}\in\mathbb{N} \\ $$$$\mid{f}_{\mathrm{4}} \left(\mathrm{1}\right)−{f}_{\mathrm{3}} \left(\mathrm{1}\right)\mid=? \\…
Question Number 329 by 123456 last updated on 23/Dec/14 $$\underset{\mathrm{0}} {\overset{{x}} {\int}}{f}\left({t}\right){dt}+\underset{{x}} {\overset{\mathrm{2}{x}} {\int}}{tf}\left({t}\right){dt}=\underset{\mathrm{0}} {\overset{\mathrm{2}{x}} {\int}}\left(\mathrm{1}−{t}\right){f}\left({t}\right){dt} \\ $$$${f}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)=? \\ $$ Commented by prakash jain last…
Question Number 316 by 123456 last updated on 25/Jan/15 $${f}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${g}:\mathbb{R}\rightarrow\mathbb{R} \\ $$$${f}\left({x}\right)=\begin{vmatrix}{{x}}&{{g}\left({x}\right)}\\{{g}\left(−{x}\right)}&{−{x}}\end{vmatrix} \\ $$$${g}\left({x}\right)=\begin{vmatrix}{{f}\left({x}\right)}&{{x}}\\{−{x}}&{{f}\left(−{x}\right)}\end{vmatrix} \\ $$ Answered by prakash jain last updated on…
Question Number 303 by 123456 last updated on 25/Jan/15 $${f}\left({x},{y},{z}\right)=\frac{{y}^{\mathrm{2}} {z}^{\mathrm{3}} }{\mathrm{1}−{x}}+\frac{{xz}^{\mathrm{3}} }{\mathrm{1}−{y}^{\mathrm{2}} }+\frac{{xy}^{\mathrm{2}} }{\mathrm{1}−{z}^{\mathrm{3}} } \\ $$$$\mathrm{find} \\ $$$$\frac{\partial{f}}{\partial{x}}+\frac{\partial{f}}{\partial{y}}+\frac{\partial{f}}{\partial{z}} \\ $$ Answered by prakash…