Question Number 140636 by Mathspace last updated on 10/May/21 $${calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)\left(\mathrm{2}{n}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$ Answered by Dwaipayan Shikari last updated on 10/May/21…
Question Number 140638 by Mathspace last updated on 10/May/21 $${let}\:{f}\left({x}\right)={arctan}\left(\frac{\mathrm{2}}{{x}}\right) \\ $$$${developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$ Answered by Dwaipayan Shikari last updated on 10/May/21 $${f}\left({x}\right)={f}\left(\mathrm{0}\right)+\frac{{f}'\left(\mathrm{0}\right)}{\mathrm{1}!}{x}+\frac{{f}''\left(\mathrm{0}\right)}{\mathrm{2}!}{x}^{\mathrm{2}} +.. \\…
Question Number 75063 by mathmax by abdo last updated on 06/Dec/19 $${calculate}\:\:\sum_{{n}=\mathrm{1}} ^{\mathrm{17}} \:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}^{\mathrm{3}} } \\ $$ Commented by mathmax by abdo last updated…
Question Number 140531 by Willson last updated on 09/May/21 $$\mathrm{Prove}\:\mathrm{that}\:\:\underset{\mathrm{0}} {\int}^{\:\mathrm{x}} \:\frac{\mathrm{t}}{\mathrm{e}^{\mathrm{t}} −\mathrm{1}}\:\mathrm{dt}\:=\:\underset{\mathrm{n}=\mathrm{1}} {\overset{+\infty} {\sum}}\:\frac{\left(\mathrm{1}−\mathrm{e}^{−\mathrm{x}} \right)^{\mathrm{n}} }{\mathrm{n}^{\mathrm{2}} } \\ $$ Answered by mathmax by abdo…
Question Number 140470 by EDWIN88 last updated on 08/May/21 $$\left(\mathrm{f}\left(\mathrm{x}\right)\right)^{\mathrm{2}} .\:\mathrm{f}\left(\frac{\mathrm{1}−\mathrm{x}}{\mathrm{1}+\mathrm{x}}\right)\:=\:\mathrm{64x}\:,\:\forall\mathrm{x}\in\mathrm{D} \\ $$$$\Rightarrow\:\mathrm{f}\left(\mathrm{x}\right)\:=? \\ $$ Answered by benjo_mathlover last updated on 08/May/21 $$\left(\mathrm{1}\right)\:\left(\mathrm{f}\left(\mathrm{x}\right)\right)^{\mathrm{2}} .\mathrm{f}\left(\frac{\mathrm{1}−\mathrm{x}}{\mathrm{1}+\mathrm{x}}\right)\:=\:\mathrm{64x} \\…
Question Number 74884 by abdomathmax last updated on 03/Dec/19 $${calculate}\:\sum_{{n}=\mathrm{1}} ^{\mathrm{20}} \:\frac{\mathrm{1}}{{n}^{\mathrm{2}} } \\ $$$$ \\ $$ Commented by mathmax by abdo last updated on…
Question Number 74887 by abdomathmax last updated on 03/Dec/19 $${calculate}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\left(−\mathrm{1}\right)^{{n}} }{\left({n}+\mathrm{1}\right){n}^{\mathrm{3}} } \\ $$ Commented by mathmax by abdo last updated on 21/Dec/19…
Question Number 74885 by abdomathmax last updated on 03/Dec/19 $${calcilate}\:\sum_{{n}=\mathrm{1}} ^{\mathrm{16}} \:\frac{\mathrm{1}}{{n}^{\mathrm{3}} } \\ $$ Answered by tw000001 last updated on 05/Dec/19 $$\mathrm{I}\:\mathrm{use}\:\mathrm{integral}\:\mathrm{to}\:\mathrm{solve}. \\ $$$$\underset{{n}=\mathrm{1}}…
Question Number 9313 by ravindra17081976@gmail.com last updated on 30/Nov/16 $$\int_{\mathrm{0}} ^{\infty} \left\{\left\{\right.\right. \\ $$ Commented by FilupSmith last updated on 30/Nov/16 $$\int_{\mathrm{0}} ^{\:\infty} \left(\right){dx}=\mathrm{0} \\…
Question Number 140387 by benjo_mathlover last updated on 07/May/21 Answered by JDamian last updated on 07/May/21 $${A}=\frac{{x}^{\mathrm{4}} }{\mathrm{2}} \\ $$ Terms of Service Privacy Policy…