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find-C-z-2-sin-z-2-dz-z-3pi-

Question Number 147406 by tabata last updated on 20/Jul/21 $${find}\:\int_{{C}} \frac{{z}+\mathrm{2}}{{sin}\left(\frac{{z}}{\mathrm{2}}\right)}{dz}\:\:\:,\mid{z}\mid=\mathrm{3}\pi \\ $$ Answered by Olaf_Thorendsen last updated on 20/Jul/21 $$\Omega\:=\:\int_{\mid{z}\mid=\mathrm{3}\pi} \frac{{z}+\mathrm{2}}{\mathrm{sin}\left(\frac{{z}}{\mathrm{2}}\right)}\:{dz} \\ $$$$\Omega\:=\:\int_{\mid{z}\mid=\mathrm{3}\pi} \frac{{z}+\mathrm{2}}{{z}}×\frac{{z}}{\mathrm{sin}\left(\frac{{z}}{\mathrm{2}}\right)}\:{dz}…

d-dn-n-

Question Number 147356 by Mrsof last updated on 20/Jul/21 $$\frac{{d}}{{dn}}\left({n}!\right) \\ $$ Answered by puissant last updated on 20/Jul/21 $$\Gamma\left({n}\right)=\left({n}−\mathrm{1}\right)!=\int_{\mathrm{0}} ^{+\infty} {t}^{{n}−\mathrm{1}} {e}^{−{t}} {dt} \\…

If-a-1-1-and-n-1-a-n-1-1-1-n-a-n-find-a-n-

Question Number 147357 by Jamshidbek last updated on 20/Jul/21 $$\:\:\mathrm{If}\:\:\mathrm{a}_{\mathrm{1}} =\mathrm{1}\:\:\mathrm{and}\:\mathrm{n}\geqslant\mathrm{1}\:\mathrm{a}_{\mathrm{n}+\mathrm{1}} =\frac{\mathrm{1}}{\mathrm{1}+\mathrm{n}\centerdot\mathrm{a}_{\mathrm{n}} } \\ $$$$\mathrm{find}\:\:\mathrm{a}_{\mathrm{n}} =? \\ $$ Answered by ArielVyny last updated on 20/Jul/21…