Category: Relation and Functions

Question Number 143254 by Mathspace last updated on 12/Jun/21 $$findthevalueof\sum _{n=1}^{\mathrm{\infty }}\frac{{(-1)}^n}{n^2(n+1)(n+2)(n+3)}$$ Answered by Olaf_Thorendsen last updated on 12/Jun/21 $${R}\left({n}\right)\:=\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)\left({n}+\mathrm{2}\right)\left({n}+\mathrm{3}\right)}…

Question Number 77616 by BK last updated on 08/Jan/20 Commented by MJS last updated on 08/Jan/20 $$\mathrm{are}\mathrm{you}\mathrm{serious}\mathrm{on}\mathrm{this}\mathrm{one}?$$$$\mathrm{serious}\left(\begin{array}{c}BK\\ \mathrm{qu}.77616\end{array}\right)=\mathrm{true}\Rightarrow BK\ne \mathrm{serious}\mathrm{\forall }\mathrm{qu}.\in {\mathbb{N}}^{★}$$ Commented by BK last…

Question Number 143147 by mathmax by abdo last updated on 10/Jun/21 $$\mathrm{montrer}\mathrm{que}\mathrm{lasuite}{\mathrm{U}}_{\mathrm{n}}=\frac{{\mathrm{H}}_{\mathrm{n}}}{{\mathrm{n}}^2}\mathrm{est}\mathrm{bornee}$$$${\mathrm{H}}_{\mathrm{n}}=\sum _{\mathrm{k}=1}^{\mathrm{n}}\frac{1}{{\mathrm{n}}^2}$$ Commented by…

Question Number 142987 by mathmax by abdo last updated on 08/Jun/21 $$\mathrm{find}\mathrm{the}\mathrm{sequence}{\mathrm{u}}_{\mathrm{n}}\mathrm{wich}\mathrm{verify}{\mathrm{u}}_{\mathrm{n}+1}={\mathrm{u}}_{\mathrm{n}}-\lambda {\mathrm{u}}_{\mathrm{n}-1}$$$$\lambda \mathrm{real}$$ Answered by Dwaipayan Shikari last updated…

Question Number 77367 by msup trace by abdo last updated on 05/Jan/20 $$letthecercle{(x+1)}^2+{(y-3)}^2=9$$$$andthepointA(4,1)$$$$vrrifythatAisoutofcircle$$$$anddeterminetheequationof$$$$twotangentestocirclewich$$$${passes}\:{by}\:{point}\:{A}.…