Question Number 7317 by lakshaysethi last updated on 24/Aug/16 $${Prove}\:{that}\:\left[\frac{{n}+\mathrm{1}}{\mathrm{2}}\right]+\left[\frac{{n}+\mathrm{2}}{\mathrm{4}}\right]+\left[\frac{{n}+\mathrm{4}}{\mathrm{8}}\right]+\left[\frac{{n}+\mathrm{8}}{\:\mathrm{16}}\right]+……..={n}. \\ $$$${Such}\:{that}\:\left[.\right]\:{denotes}\:{greatest}\:{integer}\:{function}\:{and}\:{n}\in{N}. \\ $$ Commented by FilupSmith last updated on 23/Aug/16 $${S}=\underset{{t}=\mathrm{1}} {\overset{\infty} {\sum}}\lceil\frac{{n}+\mathrm{2}^{{t}−\mathrm{1}} }{\mathrm{2}^{{t}}…
Question Number 138134 by mathmax by abdo last updated on 10/Apr/21 $$\mathrm{calculate}\:\sum_{\mathrm{n}=\mathrm{1}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{n}^{\mathrm{3}} \left(\mathrm{2n}+\mathrm{1}\right)^{\mathrm{4}} } \\ $$ Terms of Service Privacy Policy Contact:…
Question Number 6877 by sarathon last updated on 01/Aug/16 $$\mathrm{the}\:\mathrm{bottom}\left(\frac{\mathrm{1}}{\mathrm{2}}\right)\:\mathrm{of}\:\:{log}_{\frac{\mathrm{1}}{\mathrm{2}}} {x}\:\:\mathrm{wants}\:\mathrm{to}\:\mathrm{make}\:\:\mathrm{2} \\ $$$$\mathrm{2}\:\:\mathrm{how}?? \\ $$$$ \\ $$ Commented by Tawakalitu. last updated on 01/Aug/16 $${log}_{\frac{\mathrm{1}}{\mathrm{2}}}…
Question Number 72395 by mathmax by abdo last updated on 28/Oct/19 $${find}\:\sum_{{k}=\mathrm{0}} ^{{n}} \left({C}_{{n}} ^{{k}} \right)^{\mathrm{3}} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 72393 by mathmax by abdo last updated on 28/Oct/19 $${let}\:{f}\left({x}\right)\:={cos}\left({narccosx}\right) \\ $$$$\left.\mathrm{1}\right){calculate}\:{f}^{\left({n}\right)} \left({x}\right)\:{and}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{2}\right){developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$ Terms of Service Privacy Policy…
Question Number 72389 by mathmax by abdo last updated on 28/Oct/19 $${find}\:\sum_{{k}=\mathrm{1}} ^{{n}} {k}\left({C}_{{n}} ^{{k}} \right)^{\mathrm{2}} \:{interms}\:{of}\:{n} \\ $$ Answered by mind is power last…
Question Number 137817 by bramlexs22 last updated on 07/Apr/21 $${Let}\:{f}\left({x}\right)={x}^{\mathrm{2}} −\mathrm{2}{x}−\mathrm{3};\:{x}\geqslant\mathrm{1}\:\& \\ $$$${g}\left({x}\right)=\mathrm{1}+\sqrt{{x}+\mathrm{4}}\:;\:{x}\geqslant−\mathrm{4}\:{then} \\ $$$${the}\:{number}\:{of}\:{real}\:{solutions} \\ $$$${of}\:{equation}\:{f}\left({x}\right)={g}\left({x}\right)\:{is}\:… \\ $$ Answered by MJS_new last updated on…
Question Number 72260 by mathmax by abdo last updated on 26/Oct/19 $${let}\:{f}\left({x}\right)=\frac{\mathrm{2}{x}+\mathrm{3}}{{x}^{\mathrm{2}} +\mathrm{1}} \\ $$$${calculate}\:\:{f}^{\left({n}\right)} \left({x}\right) \\ $$$$\left.\mathrm{2}\right){find}\:{f}^{\left(\mathrm{10}\right)} \left({x}\right)\:{and}\:{f}^{\left(\mathrm{15}\right)} \left({x}\right) \\ $$$$\left.\mathrm{3}\right){calculate}\:{f}^{\left(\mathrm{10}\right)} \left(\mathrm{0}\right)\:{and}\:{f}^{\left(\mathrm{15}\right)} \left(\mathrm{0}\right) \\…
Question Number 72026 by mathmax by abdo last updated on 23/Oct/19 $${prove}\:{that}\:{x}^{\mathrm{4}} \:{divide}\:\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{{n}} −{nx}^{\mathrm{2}} −\mathrm{1}\:\:{without}\:{use}\:\:{binomial} \\ $$$${formula}. \\ $$ Commented by mathmax by abdo…
Question Number 72027 by mathmax by abdo last updated on 23/Oct/19 $${if}\:{a}+{b}+{c}\:=\mathrm{3}\:\:{and}\:{a}^{\mathrm{3}} \:+{b}^{\mathrm{3}} \:+{c}^{\mathrm{3}} =\mathrm{27}\:{find}\:{a}^{\mathrm{2}} \:+{b}^{\mathrm{2}} \:+{c}^{\mathrm{2}} \\ $$ Commented by Rasheed.Sindhi last updated on…