Question Number 73048 by mathmax by abdo last updated on 05/Nov/19 $${solve}\:{inside}\:{Z}^{\mathrm{2}} \:\:{x}^{\mathrm{2}} \:+\mathrm{3}{xy}−\mathrm{2}{y}^{\mathrm{2}} \:=\mathrm{122} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 73046 by mathmax by abdo last updated on 05/Nov/19 $${prove}\:{that}\:\forall{n}\:\in{N}\:\:\:\:\sum_{{k}=\mathrm{0}} ^{{n}} \:{k}\:{C}_{\mathrm{2}{n}} ^{{n}+{k}} \:={nC}_{\mathrm{2}{n}−\mathrm{1}} ^{{n}} \\ $$ Answered by mind is power last…
Question Number 73049 by mathmax by abdo last updated on 05/Nov/19 $${simplifyA}_{{n}} =\:\sum_{{k}=\mathrm{0}} ^{{n}} \left(\frac{{k}}{{n}}−\alpha\right)^{\mathrm{2}} \:{C}_{{n}} ^{{k}} \:{X}^{{k}} \left(\mathrm{1}−{X}\right)^{{n}−{k}} \\ $$ Terms of Service Privacy…
Question Number 73047 by mathmax by abdo last updated on 05/Nov/19 $${solve}\:{inside}\:{Z}^{\mathrm{3}} \:\:\:\:\:{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} \:+{z}^{\mathrm{2}\:} =\mathrm{2}{xyz} \\ $$ Answered by mind is power last updated…
Question Number 73045 by mathmax by abdo last updated on 05/Nov/19 $${calculate}\:\:\sum_{{k}=\mathrm{0}} ^{{n}} \:\frac{{C}_{{n}} ^{{k}} }{{C}_{\mathrm{2}{n}−\mathrm{1}} ^{{k}} } \\ $$ Terms of Service Privacy Policy…
Question Number 73044 by mathmax by abdo last updated on 05/Nov/19 $${prove}\:{that}\:\:\sum_{{k}=\mathrm{1}} ^{{n}} \:{H}_{{k}} =\left({n}+\mathrm{1}\right){H}_{{n}} −{n} \\ $$$${and}\:\sum_{{k}=\mathrm{1}} ^{{n}} \:{H}_{{k}} ^{\mathrm{2}} \:=\left({n}+\mathrm{1}\right){H}_{{n}} ^{\mathrm{2}} \:−\left(\mathrm{2}{n}+\mathrm{1}\right){H}_{{n}} \:+\mathrm{2}{n}…
Question Number 73043 by mathmax by abdo last updated on 05/Nov/19 $${prove}\:{that}\:{H}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\left(−\mathrm{1}\right)^{{k}+\mathrm{1}} }{{k}}×{C}_{{n}} ^{{k}} \\ $$$${H}_{{n}} =\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\mathrm{1}}{{k}} \\ $$ Commented…
Question Number 72990 by mathmax by abdo last updated on 05/Nov/19 $${calculate}\:{lim}_{{x}\rightarrow\mathrm{0}} \:\:\:\:\:\frac{{arctan}\left({e}^{{x}} \right)−\frac{\pi}{\mathrm{4}}}{{x}^{\mathrm{2}} } \\ $$ Commented by abdomathmax last updated on 19/Nov/19 $${let}\:{use}\:{hospital}\:{theorem}\:\:{f}\left({x}\right)={arctan}\left({e}^{{x}}…
Question Number 72912 by mathmax by abdo last updated on 04/Nov/19 $${calculate}\:{S}_{{p}} =\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}+{p}} \\ $$ Answered by mind is power last updated…
Question Number 7317 by lakshaysethi last updated on 24/Aug/16 $${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}}…