Define the function $f(x)=\frac{x+2}{2^x}$

$f'(x)=2^{-x}$ $(1-(x+2) ln2)$.

As $x>1$,$f'(x)<2^{-x}(1-ln8)<0$

so this function is decreasing.

Which implies the sequence $a_n$ is increasing.

Now by induction we can show that $a_n \leq 2$ for all $n$.

actually this is the limit.

## Search found 217 matches

- Mon Feb 11, 2013 10:11 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2013: Higher Secondary 8
- Replies:
**6** - Views:
**3566**

### Re: BdMO 2013 Higher Secondary Problem 8

$A$,$X$,$C$,$Y$ cyclic.And $Z$,$X$,$S$,$Y$ cyclic.So $EZ.ES$=$EX.EY$=$EA.EC$ Let $H$ be the orthocentre.$EA.EC=EH.EB$ But $ES.EZ=EH.EB$ so $H$ is the orthocentre of $\triangle ZBS$ So $ZH$ is perpendicular to $BS$. Let $M$ be the midpoint of $AC$. $ZH$ is the polar of $B$ with respect to circle $AFD...

- Sat Feb 02, 2013 12:07 am
- Forum: Algebra
- Topic: Fuctional inequality
- Replies:
**1** - Views:
**1193**

### Re: Fuctional inequality

Telescoping yields an elegant solution.

- Fri Feb 01, 2013 10:52 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2012: Secondary 8
- Replies:
**10** - Views:
**4948**

### Re: BdMO National 2012: Secondary 8

That's what stops the good ninja(me).Mis-comprehension of problem statement.

Now i know how the hell u deduce those things.

Now i know how the hell u deduce those things.

- Fri Feb 01, 2013 10:23 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2012: Secondary 8
- Replies:
**10** - Views:
**4948**

### Re: BdMO National 2012: Secondary 8

I don't know how the hell you deduced $EA=EE"$

Because that implies $\angle E'AE"$ $=90 ^\circ$ which is not true.

Because that implies $\angle E'AE"$ $=90 ^\circ$ which is not true.

- Fri Feb 01, 2013 10:04 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO National 2012: Secondary 8
- Replies:
**10** - Views:
**4948**

### Re: BdMO National 2012: Secondary 8

I don't know how the hell you deduced that $\angle ECA=2\angle EAC$.Please explain.

Your solution is incorrect.

Your solution is incorrect.

- Thu Jan 31, 2013 7:11 pm
- Forum: National Math Olympiad (BdMO)
- Topic: BdMO Higher secondary solutions
- Replies:
**13** - Views:
**10572**

### Re: BdMO Higher secondary solutions

এই কথা পড়ে আমার হাসি পাচ্ছে।TIUrmi wrote:ইতিহাসে আমার নাম স্বর্ণাক্ষরে লেখা থাকবে সেই আনন্দে আমার কান্না পাচ্ছে।

- Wed Jan 30, 2013 2:30 pm
- Forum: Divisional Math Olympiad
- Topic: Rajshahi MO 2013, Secondary 1
- Replies:
**9** - Views:
**3804**

### Re: Rajshahi MO 2013, Secondary 1

Oi Mahi,that makes use of such a big assumption as for those $4$ points ,the diagonals intersect strictly inside the hull.But we can get $3$ intersection points.Namely for points $A$,$B$,$C$,$D$ ,$AB \cap CD$ ,$AD \cap BC$ and $AC \cap BD$.

- Sat Jan 26, 2013 12:16 am
- Forum: Primary Level
- Topic: palindrome number
- Replies:
**5** - Views:
**6442**

### Re: palindrome number

Prosenjit,

Your solution is close to brute force.you have to show that 11 must divide them.Eventually in order to be a perfect square 121 must divide them.Which is not possible.

Your solution is close to brute force.you have to show that 11 must divide them.Eventually in order to be a perfect square 121 must divide them.Which is not possible.

- Fri Jan 25, 2013 11:31 pm
- Forum: Geometry
- Topic: Geometry Marathon v1.0
- Replies:
**23** - Views:
**10955**

### Re: Geometry Marathon v1.0

I like this marathon.I am so glad that i am posting in the same marathon as our predecessors.

Why don't we run this marathon?

Why don't we run this marathon?