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Question-142437

Question Number 142437 by mohammad17 last updated on 31/May/21 Answered by Dwaipayan Shikari last updated on 31/May/21 $$\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}}{{n}}\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\sqrt{\frac{{n}}{{n}+{r}}}\: \\ $$$$=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}}{\:\sqrt{\mathrm{1}+{x}}}{dx}\:\:\:\:\mathrm{1}+{x}={u}^{\mathrm{2}}…

Question-11341

Question Number 11341 by Nadium last updated on 21/Mar/17 Commented by FilupS last updated on 22/Mar/17 $$\Omega=\underset{{n}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{1}}{{n}^{\mathrm{4}} }\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\left(\underset{{j}=\mathrm{1}} {\overset{{n}} {\sum}}\left({i}^{\mathrm{2}} +{j}^{\mathrm{2}} \right)\mid{i}^{\mathrm{2}}…

x-x-4-5-x-7-7-x-5-x-

Question Number 142415 by Rankut last updated on 31/May/21 $$\frac{{x}}{{x}+\mathrm{4}}=\frac{\mathrm{5}\lfloor{x}\rfloor−\mathrm{7}}{\mathrm{7}\lfloor{x}\rfloor−\mathrm{5}} \\ $$$${x}=? \\ $$ Answered by mr W last updated on 31/May/21 $${say}\:{x}={n}+{f} \\ $$$$\frac{{n}+{f}}{{n}+{f}+\mathrm{4}}=\frac{\mathrm{5}{n}−\mathrm{7}}{\mathrm{7}{n}−\mathrm{5}}…