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Category: Integration

decompose-F-x-1-x-n-1-x-2-x-1-dans-C-x-puis-dans-R-x-

Question Number 147682 by mathmax by abdo last updated on 22/Jul/21 $$\mathrm{decompose}\:\mathrm{F}\left(\mathrm{x}\right)=\frac{\mathrm{1}}{\left(\mathrm{x}^{\mathrm{n}} −\mathrm{1}\right)\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{x}+\mathrm{1}\right)}\:\mathrm{dans}\:\mathrm{C}\left(\mathrm{x}\right)\:\mathrm{puis}\:\mathrm{dans}\:\mathrm{R}\left(\mathrm{x}\right) \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Question-147670

Question Number 147670 by mnjuly1970 last updated on 22/Jul/21 Answered by Olaf_Thorendsen last updated on 22/Jul/21 $$\mathrm{By}\:\mathrm{definition}\:\mathrm{H}_{{n}} ^{\left(\mathrm{2}\right)} \:=\:\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}\frac{\mathrm{1}}{{k}^{\mathrm{2}} } \\ $$$$\Rightarrow\:\mathrm{H}_{{n}−\mathrm{1}} ^{\left(\mathrm{2}\right)}…

1-i-1-n-j-1-n-i-j-2-i-1-n-j-i-n-1-j-3-i-1-n-2-i-

Question Number 147576 by qaz last updated on 22/Jul/21 $$\left(\mathrm{1}\right)::\:\:\:\:\:\underset{\mathrm{i}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\underset{\mathrm{j}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\mid\mathrm{i}−\mathrm{j}\mid=? \\ $$$$\left(\mathrm{2}\right)::\:\:\:\:\:\underset{\mathrm{i}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\underset{\mathrm{j}=\mathrm{i}} {\overset{\mathrm{n}} {\sum}}\frac{\mathrm{1}}{\mathrm{j}}=? \\ $$$$\left(\mathrm{3}\right)::\:\:\:\:\:\:\underset{\mathrm{i}=\mathrm{1}} {\overset{\mathrm{n}^{\mathrm{2}} } {\sum}}\left[\sqrt{\mathrm{i}}\right]=?…

calculate-I-n-1-n-n-e-x-2-3y-2-dxdy-and-find-lim-n-I-n-conclude-that-0-e-x-2-dx-pi-2-

Question Number 81996 by msup trace by abdo last updated on 17/Feb/20 $${calculate}\:{I}_{{n}} =\int\int_{\left[\frac{\mathrm{1}}{{n}},{n}\left[\right.\right.} \:\:{e}^{−{x}^{\mathrm{2}} −\mathrm{3}{y}^{\mathrm{2}} } {dxdy} \\ $$$${and}\:{find}\:{lim}_{{n}\rightarrow+\infty} \:\:{I}_{{n}} \\ $$$${conclude}\:{that}\:\int_{\mathrm{0}} ^{\infty} \:{e}^{−{x}^{\mathrm{2}}…

calculate-D-ln-1-x-y-dxdy-with-D-is-the-triangle-limited-by-points-0-A-1-0-and-B-0-1-

Question Number 81993 by msup trace by abdo last updated on 17/Feb/20 $${calculate}\:\int\int_{{D}} {ln}\left(\mathrm{1}+{x}+{y}\right){dxdy} \\ $$$${with}\:{D}\:{is}\:{the}\:{triangle}\:{limited}\:{by} \\ $$$${points}\:\mathrm{0},{A}\left(\mathrm{1},\mathrm{0}\right)\:{and}\:{B}\left(\mathrm{0},\mathrm{1}\right) \\ $$ Terms of Service Privacy Policy…