## Binomial and power of 4(or 2?)

For discussing Olympiad Level Algebra (and Inequality) problems
Masum
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Joined: Tue Dec 07, 2010 1:12 pm

### Binomial and power of 4(or 2?)

Prove that, $4^n<(n+1)(2n+1)\binom n{\left\lfloor \frac n2\right\rfloor}^2$.
Hint: see the title
One one thing is neutral in the universe, that is $0$.

*Mahi*
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### Re: Binomial and power of 4(or 2?)

Typo?
$\binom{5}{2} \cdot 6 \cdot 11 = 660 < 4^5$

Use $L^AT_EX$, It makes our work a lot easier!

Masum
Posts: 592
Joined: Tue Dec 07, 2010 1:12 pm

### Re: Binomial and power of 4(or 2?)

Fixed. Now it's ok
One one thing is neutral in the universe, that is $0$.

nayel
Posts: 268
Joined: Tue Dec 07, 2010 7:38 pm
Location: Dhaka, Bangladesh or Cambridge, UK

### Re: Binomial and power of 4(or 2?)

Same idea from the other thread gives a stronger bound:
"Everything should be made as simple as possible, but not simpler." - Albert Einstein