## Search found 155 matches

- Tue Oct 14, 2014 9:00 pm
- Forum: Combinatorics
- Topic: Solution to a Non-Linear Recurrence
- Replies:
**4** - Views:
**2619**

### 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:
**2619**

### 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:
**2619**

### 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:
**2343**

### 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:
**5422**

### 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:
**2414**

### 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:
**9731**

### 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:
**8654**

### 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:
**2007**

### 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:
**2007**