Search found 155 matches
- Tue Oct 14, 2014 9:00 pm
- Forum: Combinatorics
- Topic: Solution to a Non-Linear Recurrence
- Replies: 4
- Views: 4343
Re: Solution to a Non-Linear Recurrence
Any help...
- Mon Oct 13, 2014 3:11 pm
- Forum: Combinatorics
- Topic: Solution to a Non-Linear Recurrence
- Replies: 4
- Views: 4343
Re: Solution to a Non-Linear Recurrence
To tell the truth, it's a product of my thought... I came up with this recurrence while trying to find the Equivalent Resistance of an Infinite Fractal-Circuit that I made up. :roll: The original recurrence I was trying to solve had $c=3, c_1=4, c_2=-2, c_3=-2$ and $a_0=\frac{2}{3}$. I was wondering...
- Sun Oct 12, 2014 8:32 pm
- Forum: Combinatorics
- Topic: Solution to a Non-Linear Recurrence
- Replies: 4
- Views: 4343
Solution to a Non-Linear Recurrence
Let $(a_n)$ be a sequence of numbers which satisfies the following recurrence relation for all $n\geq 1$, \[c\cdot a_na_{n-1} + c_1\cdot a_n + c_2\cdot a_{n-1} + c_3=0 \] where, $c_1, c_2, c_3$ and $c$ are constants, $c\neq 0$, and $a_0\neq-\frac{c_1}{c}$ is given. Does a general solution in CLOSED ...
- Fri Oct 03, 2014 11:04 pm
- Forum: Secondary Level
- Topic: Directed Angle
- Replies: 3
- Views: 4015
Re: Directed Angle
I think this might help...
Courtesy of R. A. Johnson, MAA, and, JSTOR :
http://www.jstor.org/stable/2973001
Courtesy of R. A. Johnson, MAA, and, JSTOR :
http://www.jstor.org/stable/2973001
- Tue Aug 26, 2014 1:09 am
- Forum: Physics
- Topic: Resultant Resistance
- Replies: 2
- Views: 7084
Re: Resultant Resistance
This might help...It has some wonderful uses of symmetries in Electric Circuits:
Resistors Cube Problems
Resistors Cube Problems
- Thu Aug 21, 2014 6:40 pm
- Forum: Algebra
- Topic: Proofathon Inequality
- Replies: 4
- Views: 4073
Re: Proofathon Inequality
Straightforward Jensen... Let, $f(x)=\sqrt{1+x^2}\Rightarrow f''(x)=(1+x^2)^{-\frac{3}{2}}> 0 \; \forall x\in \mathbb{R}$ $\therefore f(x)$ is convex. So, \[\frac{\sum_{k=1}^n f(k)}{n}\geq f\left(\frac{\sum_{k=1}^n k}{n}\right)\] \[\Rightarrow \sum_{k=1}^n\sqrt{k^2+1}\geq n\cdot f\left(\frac{n+1}{2}...
- Thu Feb 13, 2014 7:50 pm
- Forum: Social Lounge
- Topic: Best of Luck :)
- Replies: 2
- Views: 14309
Best of Luck :)
Best of luck to all the participants of BDMO 2014. Sleep well, keep your head clear and give it your best...
- Thu Feb 13, 2014 7:31 pm
- Forum: National Math Olympiad (BdMO)
- Topic: warm-up problems for national BdMO'14
- Replies: 25
- Views: 16095
Re: warm-up problems for national BdMO'14
Solution to Problem 12: Lemma: If $G$ is the centroid of $\triangle ABC$, $E, F$ the mid-points of $AB, AC$, and, $AG \cap EF=S$, then, $GS:SA=1:3$ and $S$ is the mid-point of $EF$. Proof of Lemma: If $M$ is the mid-point of $BC$, then, $G$ is also the centroid of $\triangle MEF$. $\therefore GS=2G...
- Thu Feb 13, 2014 6:30 pm
- Forum: Geometry
- Topic: Touching Circumcircles around Incentre [Self-Made]
- Replies: 4
- Views: 3414
Re: Touching Circumcircles around Incentre [Self-Made]
Nice solution
It was inspired from JBMO 1997 #3.
It was inspired from JBMO 1997 #3.
- Wed Feb 12, 2014 2:58 pm
- Forum: Geometry
- Topic: Touching Circumcircles around Incentre [Self-Made]
- Replies: 4
- Views: 3414