Category: Arithmetic

Question Number 8558 by Sopheak last updated on 16/Oct/16 Commented by FilupSmith last updated on 16/Oct/16 $$S_n=\underset{k=1}{\sum ^n}\frac{k^4}{(2k-1)(2k+1)}$$$$\frac{1}{(2k-1)(2k+1)}=\frac{A}{2k-1}+\frac{B}{2k+1}$$$$\mathrm{1}={A}\left(\mathrm{2}{k}+\mathrm{1}\right)+{B}\left(\mathrm{2}{k}−\mathrm{1}\right)…

Question Number 139548 by peter frank last updated on 28/Apr/21 Answered by Dwaipayan Shikari last updated on 28/Apr/21 $$\int_{−\frac{\pi}{\mathrm{2}}} ^{\frac{\pi}{\mathrm{2}}} \frac{{x}^{\mathrm{2}} {sin}\left({x}\right)}{\mathrm{1}+{x}^{\mathrm{6}} }{dx}=−\int_{−\frac{\pi}{\mathrm{2}}} ^{\frac{\pi}{\mathrm{2}}} \frac{{x}^{\mathrm{2}}…

Question Number 73818 by rajesh4661kumar@gmail.com last updated on 16/Nov/19 Commented by Tinku Tara last updated on 16/Nov/19 $$\mathrm{Can}\mathrm{you}\mathrm{post}\mathrm{a}\mathrm{clear}\mathrm{image}.$$ Answered by Tanmay chaudhury last…

Question Number 8232 by FilupSmith last updated on 03/Oct/16 $$\mathrm{Every}\mathrm{day},\mathrm{for}n\mathrm{days},\mathrm{you}\mathrm{put}\mathrm{either}$$$$\mathrm{\$}1,\mathrm{\$}2,\mathrm{or}\mathrm{\$}3\mathrm{into}\mathrm{a}\mathrm{saving}\mathrm{account}.$$$$\mathrm{It}\mathrm{is}\mathrm{random}\mathrm{as}\mathrm{to}\mathrm{how}\mathrm{much}\mathrm{you}\mathrm{save}$$$$\mathrm{each}\mathrm{day}.\mathrm{What}\mathrm{is}\mathrm{the}average\mathrm{amount}$$$$\mathrm{you}\mathrm{will}\mathrm{have}\mathrm{saved}\mathrm{in}n\mathrm{days}?$$ Answered by prakash jain last…

Question Number 138989 by metamorfose last updated on 20/Apr/21 $$findtheintegersx,y,z,nthat$$$$satisfy:2^n=x!+y!+z!$$ Answered by mindispower last updated on 21/Apr/21 $$letm=min(x,y,z),ifm⩾3\Rightarrow$$$${x}!+{y}!+{z}!\equiv\mathrm{0}\left[\mathrm{3}\right]\Leftrightarrow\mathrm{2}^{{n}}…