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Category: Algebra

n-1-1-n-2-1-1-2-1-3-1-n-2-

Question Number 147737 by liberty last updated on 23/Jul/21 $$\:\underset{{n}\geqslant\mathrm{1}} {\sum}\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+…+\frac{\mathrm{1}}{{n}}\right)^{\mathrm{2}} =? \\ $$ Answered by ArielVyny last updated on 24/Jul/21 $$\left(\underset{{n}\geqslant\mathrm{1}} {\sum}\frac{\mathrm{1}}{{n}}\right)^{\mathrm{2}} \leqslant\Sigma\frac{\mathrm{1}}{{n}^{\mathrm{2}}…

f-0-f-1-f-2-f-n-n-n-a-f-16-15-15-1-find-a-

Question Number 147697 by mathdanisur last updated on 22/Jul/21 $${f}\left(\mathrm{0}\right)+{f}\left(\mathrm{1}\right)+{f}\left(\mathrm{2}\right)+…+{f}\left({n}\right)={n}!−{n}\centerdot{a} \\ $$$${f}\left(\mathrm{16}\right)=\mathrm{15}\centerdot\left(\mathrm{15}!−\mathrm{1}\right) \\ $$$${find}\:\:\boldsymbol{{a}}=? \\ $$ Answered by Olaf_Thorendsen last updated on 22/Jul/21 $$\underset{{k}=\mathrm{0}} {\overset{{n}}…

234-5-23-5-x-5-x-

Question Number 147689 by mathdanisur last updated on 22/Jul/21 $$\left(\mathrm{234}\right)_{\mathrm{5}} \:\centerdot\:\left(\mathrm{23}\right)_{\mathrm{5}} \:=\:\left({x}\right)_{\mathrm{5}} \:\:\Rightarrow\:\:\boldsymbol{{x}}=? \\ $$ Answered by Olaf_Thorendsen last updated on 22/Jul/21 $$\left(\mathrm{234}\right)_{\mathrm{5}} .\left(\mathrm{23}\right)_{\mathrm{5}} \\…

Question-147673

Question Number 147673 by mnjuly1970 last updated on 22/Jul/21 Answered by Rasheed.Sindhi last updated on 22/Jul/21 $$\sqrt[{\mathrm{3}}]{{x}}+\sqrt[{\mathrm{3}}]{{x}−\mathrm{2}}=\sqrt[{\mathrm{3}}]{{x}−\mathrm{1}} \\ $$$$\left(\sqrt[{\mathrm{3}}]{{x}}+\sqrt[{\mathrm{3}}]{{x}−\mathrm{2}}\right)^{\mathrm{3}} =\left(\sqrt[{\mathrm{3}}]{{x}−\mathrm{1}}\right)^{\mathrm{3}} \\ $$$${x}+{x}−\mathrm{2}+\mathrm{3}\sqrt[{\mathrm{3}}]{{x}}\sqrt[{\mathrm{3}}]{{x}−\mathrm{2}}\left(\sqrt[{\mathrm{3}}]{{x}}+\sqrt[{\mathrm{3}}]{{x}−\mathrm{2}}\right)={x}−\mathrm{1} \\ $$$$\mathrm{3}\sqrt[{\mathrm{3}}]{{x}}\sqrt[{\mathrm{3}}]{{x}−\mathrm{2}}\left(\sqrt[{\mathrm{3}}]{{x}−\mathrm{1}}\right)=−{x}+\mathrm{1} \\…

Solve-simultaneously-x-2-y-2-61-equation-i-x-3-y-3-91-equation-ii-

Question Number 16600 by tawa tawa last updated on 24/Jun/17 $$\mathrm{Solve}\:\mathrm{simultaneously} \\ $$$$\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{y}^{\mathrm{2}} \:=\:\mathrm{61}\:\:\:\:\:\:\:\:\:…………..\:\mathrm{equation}\:\left(\mathrm{i}\right) \\ $$$$\mathrm{x}^{\mathrm{3}} \:−\:\mathrm{y}^{\mathrm{3}} \:=\:\mathrm{91}\:\:\:\:\:\:\:\:\:…………..\:\mathrm{equation}\:\left(\mathrm{ii}\right) \\ $$ Commented by prakash jain…

In-an-arrangement-of-the-word-VIOLENT-find-the-chances-that-the-vowels-I-O-E-occupy-the-odd-positions-

Question Number 82130 by TawaTawa last updated on 18/Feb/20 $$\mathrm{In}\:\mathrm{an}\:\mathrm{arrangement}\:\mathrm{of}\:\mathrm{the}\:\mathrm{word}\:\:\mathrm{VIOLENT},\:\mathrm{find}\:\mathrm{the}\:\mathrm{chances} \\ $$$$\mathrm{that}\:\mathrm{the}\:\mathrm{vowels}\:\:\:\mathrm{I},\:\mathrm{O},\:\mathrm{E}\:\:\:\mathrm{occupy}\:\mathrm{the}\:\mathrm{odd}\:\mathrm{positions}. \\ $$ Commented by mr W last updated on 18/Feb/20 $${we}\:{have}\:\mathrm{4}\:{odd}\:{positions}:\:\mathrm{1},\:\mathrm{3},\:\mathrm{5},\:\mathrm{7} \\ $$$${we}\:{have}\:\mathrm{3}\:{even}\:{positions}:\:\mathrm{2},\:\mathrm{4},\:\mathrm{6}…