Category: Relation and Functions

Question Number 72021 by mathmax by abdo last updated on 23/Oct/19 $$calculateintermsofn{U}_n=\sum _{1⩽i<j⩽n}sin\left(\frac{i\pi }{n}\right)sin\left(\frac{j\pi }{n}\right)$$ Commented by mathmax by abdo last updated on 26/Oct/19…

Question Number 72018 by mathmax by abdo last updated on 23/Oct/19 $$calculate\sum _{n=1}^{\mathrm{\infty }}\frac{{(-1)}^n}{n^3{(n+1)}^2}$$ Commented by mathmax by abdo last…

Question Number 137365 by liberty last updated on 02/Apr/21 $$Givenf(x^2+x)+2f(x^2-3x+2)=9x^2-15x$$$$findthevalueoff\left(2017\right).$$ Answered by MJS_new last updated on 02/Apr/21 $${f}\left({t}\right)={at}+{b}…

Question Number 6267 by sanusihammed last updated on 21/Jun/16 $$Verifytheconvergenceoftheexponentialseries{e}^x$$$$using{D}^{\prime }Alermbertratiotest.$$ Commented by Yozzii last updated on 21/Jun/16 $${u}_{{r}} =\frac{{x}^{{r}} }{{r}!}\Rightarrow\frac{{u}_{{r}+\mathrm{1}} }{{u}_{{r}}…

Question Number 6238 by sanusihammed last updated on 19/Jun/16 Answered by Yozzii last updated on 20/Jun/16 $$Let\underset{n\to \mathrm{\infty }}{\lim }{(1+n^{-1})}^{-n^2}=l.$$$${Let}\:{u}={n}^{−\mathrm{1}} \Rightarrow{l}=\underset{{u}\rightarrow\mathrm{0}^{+} }…