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Category: Arithmetic

prove-the-compact-form-of-multivariable-Taylor-series-T-B-n-1-n-2-n-d-0-i-0-n-d-x-i-d-i-i-0-n-d-n-i-i-0-n-d-x-i-f-

Question Number 98116 by  M±th+et+s last updated on 11/Jun/20 $${prove}\:{the}\:{compact}\:{form}\:{of}\:{multivariable} \\ $$$${Taylor}\:{series} \\ $$$$ \\ $$$$\left({T}\ast{B}\right)=\underset{{n}=\mathrm{1},{n}=\mathrm{2}..{n}_{{d}} =\mathrm{0}} {\overset{\infty} {\sum}}\frac{\prod_{\mathrm{i}=\mathrm{0}} ^{{n}_{{d}} } \left({x}_{\mathrm{i}} −{d}_{\mathrm{i}} \right)}{\prod_{\mathrm{i}=\mathrm{0}} ^{{n}_{{d}}…

show-that-n-1-arctan-2-n-2-3pi-4-

Question Number 98060 by  M±th+et+s last updated on 11/Jun/20 $${show}\:{that} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}{arctan}\left(\frac{\mathrm{2}}{{n}^{\mathrm{2}} }\right)=\frac{\mathrm{3}\pi}{\mathrm{4}} \\ $$ Answered by smridha last updated on 11/Jun/20 $${is}\:{it}\:\boldsymbol{{right}}\:\boldsymbol{{ans}}???\boldsymbol{{I}}\:{think}\:\boldsymbol{{it}}'{s}\:{just}…

prove-n-1-9n-4-3n-3n-1-3n-2-3-2-ln-3-

Question Number 97956 by  M±th+et+s last updated on 10/Jun/20 $${prove} \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{9}{n}+\mathrm{4}}{\mathrm{3}{n}\left(\mathrm{3}{n}+\mathrm{1}\right)\left(\mathrm{3}{n}+\mathrm{2}\right)}=\frac{\mathrm{3}}{\mathrm{2}}−{ln}\left(\mathrm{3}\right) \\ $$ Answered by maths mind last updated on 13/Jun/20 $$=\underset{{n}\geqslant\mathrm{1}}…