Question Number 73042 by mathmax by abdo last updated on 05/Nov/19 $${prove}\:{that}\:{for}\:\left({n},{p}\right)\in{N}^{\bigstar^{\mathrm{2}} } \:\:\:\sum_{{k}=\mathrm{0}} ^{{p}\:} \:{k}\:{C}_{{n}} ^{{p}−{k}} \:{C}_{{n}} ^{{k}} \:={n}\:{C}_{\mathrm{2}{n}−\mathrm{1}} ^{{p}−\mathrm{1}} \\ $$$${conclude}\:{the}\:{value}\:{of}\:\sum_{{k}=\mathrm{0}} ^{{n}} \:{k}\:\left({C}_{{n}}…
Question Number 73041 by mathmax by abdo last updated on 05/Nov/19 $${prove}\:{that}\:\forall{n}\in\:{N}\:\:\sum_{{k}=\mathrm{0}} ^{\mathrm{2}{n}} \:\left(−\mathrm{1}\right)^{{k}} \:\left({C}_{\mathrm{2}{n}} ^{{k}} \right)^{\mathrm{2}} \:=\left(−\mathrm{1}\right)^{{n}} \:{C}_{\mathrm{2}{n}} ^{{n}} \\ $$ Commented by mathmax…
Question Number 73040 by mathmax by abdo last updated on 05/Nov/19 $${prove}\:{that}\:\:\forall\left({n},{p}\right)\in{N}^{\bigstar} ×{N} \\ $$$$\left.\mathrm{1}\right)\sum_{{k}=\mathrm{0}} ^{{p}} \:\left(−\mathrm{1}\right)^{{k}} \:{C}_{{n}} ^{{k}} \:=\left(−\mathrm{1}\right)^{{p}} \:{C}_{{n}−\mathrm{1}} ^{{p}} \\ $$$$\left.\mathrm{2}\right)\forall\left({p},{q}\right)\in{N}^{\mathrm{2}} \:\:\:\:\sum_{{k}=\mathrm{0}}…
Question Number 73039 by mathmax by abdo last updated on 05/Nov/19 $${let}\:{U}_{{n}} =\frac{{n}}{\mathrm{2}}\:{if}\:{n}\:{even}\:{and}\:{U}_{{n}} =\frac{{n}−\mathrm{1}}{\mathrm{2}}\:{if}\:{n}\:{odd}\:{let}\:{f}\left({n}\right)=\sum_{{k}=\mathrm{0}} ^{{n}} {U}_{{k}} \\ $$$${prove}\:{that}\:\forall\left({x},{y}\right)\in{N}^{\mathrm{2}} \:\:\:\:{f}\left({x}+{y}\right)−{f}\left({x}−{y}\right)={xy} \\ $$ Answered by mind is…
Question Number 73036 by mathmax by abdo last updated on 05/Nov/19 $$\left.{calculate}\:\mathrm{1}\right)\:\sum_{{k}=\mathrm{1}} ^{{n}} \:{k}^{\mathrm{2}} \left({n}+\mathrm{1}−{k}\right) \\ $$$$\left.\mathrm{2}\right)\sum_{\mathrm{1}\leqslant{i}\leqslant{j}\leqslant{n}} \:{ij} \\ $$ Commented by mathmax by abdo…
Question Number 7500 by Tawakalitu. last updated on 31/Aug/16 $$\mathrm{5}^{\sqrt{{x}\:}} \:−\:\:\mathrm{5}^{{x}\:−\:\mathrm{7}} \:\:=\:\:\mathrm{100} \\ $$$$ \\ $$$${Find}\:{the}\:{value}\:{of}\:{x}. \\ $$$${x}\:=\:\mathrm{9}\:\:\:{please}\:{workings}. \\ $$ Answered by sandy_suhendra last updated…
Question Number 73034 by mathmax by abdo last updated on 05/Nov/19 $${calculate}\:{U}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{{k}}{\left({k}+\mathrm{1}\right)!} \\ $$ Commented by mathmax by abdo last updated on…
Question Number 73032 by mathmax by abdo last updated on 05/Nov/19 $${find}\:{x}\:{from}\:{n}\:\:/\:\exists{n}\in{N}^{{n}} \:\:\:\:{and}\:\mathrm{1}+{x}+{x}^{\mathrm{2}} \:+{x}^{\mathrm{3}} \:+{x}^{\mathrm{4}} ={n}^{\mathrm{2}} \\ $$ Answered by mind is power last updated…
Question Number 73035 by mathmax by abdo last updated on 05/Nov/19 $${prove}\:{that}\:\:\forall{n}\in{N}^{\bigstar} \:\:\:\:\:\mathrm{2}!\mathrm{4}!….\left(\mathrm{2}{n}\right)!\geqslant\left\{\left({n}+\mathrm{1}\right)!\right\}^{{n}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 73033 by mathmax by abdo last updated on 05/Nov/19 $${solve}\:{inside}\:{N}^{\mathrm{2}} \:\:\:\:{x}\left({x}+\mathrm{1}\right)=\mathrm{4}{y}\left({y}+\mathrm{1}\right) \\ $$ Answered by mind is power last updated on 05/Nov/19 $$\Leftrightarrow\mathrm{4x}\left(\mathrm{x}+\mathrm{1}\right)=\mathrm{16y}\left(\mathrm{y}+\mathrm{1}\right)…