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Question-194241

Question Number 194241 by tri26112004 last updated on 01/Jul/23 Answered by mr W last updated on 02/Jul/23 $${assumed}\:{a},{b}\in{N} \\ $$$$\frac{\mathrm{1}}{{n}\left({n}+{a}\right)\left({n}+{b}\right)}=\frac{{A}}{{n}}+\frac{{B}}{{n}+{a}}+\frac{{C}}{{n}+{b}} \\ $$$$\left({A}+{B}+{C}\right){n}^{\mathrm{2}} +\left[\left(\mathrm{2}{a}+{b}\right){A}+{bB}\right]{n}+{abA}=\mathrm{1} \\ $$$${A}+{B}+{C}=\mathrm{0}…

how-to-evaluate-n-0-1-n-k-n-n-zn-1-

Question Number 194237 by MrGHK last updated on 01/Jul/23 $$\boldsymbol{\mathrm{how}}\:\boldsymbol{\mathrm{to}}\:\boldsymbol{\mathrm{evaluate}}\: \\ $$$$\underset{{n}=\mathrm{0}} {\overset{\infty} {\boldsymbol{\sum}}}\frac{\left(−\mathrm{1}\right)^{{n}} }{{k}^{{n}} {n}!\left({zn}+\mathrm{1}\right)} \\ $$ Commented by TheHoneyCat last updated on 14/Jul/23…

Question-194236

Question Number 194236 by MrGHK last updated on 01/Jul/23 Answered by witcher3 last updated on 03/Jul/23 $$\mathrm{S}=\underset{\mathrm{n}\geqslant\mathrm{0}} {\sum}\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{n}!\left(\mathrm{zn}+\mathrm{1}\right)\mathrm{k}^{\mathrm{n}} } \\ $$$$=\underset{\mathrm{n}\geqslant\mathrm{0}} {\sum}\int\left(\frac{−\mathrm{1}}{\mathrm{k}}\right)^{\mathrm{n}} .\frac{\mathrm{1}}{\mathrm{n}!}\int_{\mathrm{0}} ^{\mathrm{1}}…

n-1-1-n-n-15-n-30-

Question Number 194183 by tri26112004 last updated on 29/Jun/23 $$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{{n}\left({n}+\mathrm{15}\right)\left({n}+\mathrm{30}\right)} \\ $$ Answered by ARUNG_Brandon_MBU last updated on 29/Jun/23 $$\frac{\mathrm{1}}{{n}\left({n}+\mathrm{15}\right)\left({n}+\mathrm{30}\right)}=\frac{\mathrm{1}}{\mathrm{450}{n}}−\frac{\mathrm{1}}{\mathrm{225}\left({n}+\mathrm{15}\right)}+\frac{\mathrm{1}}{\mathrm{450}\left({n}+\mathrm{30}\right)} \\ $$$${S}=\frac{\mathrm{1}}{\mathrm{450}}\underset{{n}=\mathrm{0}} {\overset{\infty}…

Question-194064

Question Number 194064 by Abdullahrussell last updated on 27/Jun/23 Answered by som(math1967) last updated on 27/Jun/23 $$\left.{i}\left.\right)×{asec}\theta\:−{ii}\right)×\frac{{cos}\theta}{{a}} \\ $$$$\:\frac{{ay}}{{b}}{tan}\theta\:+\frac{{by}}{{a}}{cot}\theta={asec}\theta−\frac{{cos}\theta}{{a}}+\frac{{b}^{\mathrm{2}} {cos}\theta}{{a}} \\ $$$${y}\left(\frac{{a}^{\mathrm{2}} {tan}^{\mathrm{2}} \theta+{b}^{\mathrm{2}} }{{abtan}\theta}\right)=\frac{{a}^{\mathrm{2}}…

f-x-f-x-1-x-1-f-6-solution-

Question Number 194085 by 073 last updated on 27/Jun/23 $$\mathrm{f}\left(\mathrm{x}\right)−\mathrm{f}\left(\mathrm{x}−\mathrm{1}\right)=\mathrm{x}+\mathrm{1} \\ $$$$\mathrm{f}'\left(\mathrm{6}\right)=? \\ $$$$\mathrm{solution}?? \\ $$ Answered by qaz last updated on 27/Jun/23 $${f}\left({x}\right)={ax}^{\mathrm{2}} +{bx}+{c}…