QM$\geq$AM$\geq $GM$\geq $HM
$\sqrt{\frac{x_{1}^{2}+x_{2}^{2}+\cdot \cdot \cdot +x_{n}^{2}}{n}} \geq \frac{x_{1}+x_{2}+\cdot \cdot \cdot +x_{n}}{n}\geq \sqrt[n]{x_{1}x_{2}\cdot \cdot \cdot x_{n}}\geq \frac{n}{\frac{1}{x_{1}}+\frac{1}{x_{2}}+\cdot \cdot \cdot \frac{1}{x_{n}}}$
I think it is a good and useful relation to discuss
inequality of means (bomc)
-
nafistiham
- Posts:829
- Joined:Mon Oct 17, 2011 3:56 pm
- Location:24.758613,90.400161
- Contact:
Last edited by nafistiham on Sun Oct 30, 2011 6:41 pm, edited 1 time in total.
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Re: inequality of means (bomc)
Please read Forum Guide and Rules before you post.
Use $L^AT_EX$, It makes our work a lot easier!
Nur Muhammad Shafiullah | Mahi
Use $L^AT_EX$, It makes our work a lot easier!
Nur Muhammad Shafiullah | Mahi
-
nafistiham
- Posts:829
- Joined:Mon Oct 17, 2011 3:56 pm
- Location:24.758613,90.400161
- Contact:
Re: inequality of means (bomc)
হায় হায় আমার ৫০ নাম্বার পোস্টে ভুল ঠিক করতে হচ্চে।কারন উপরের পোস্ট টা এডিট করা যাবে না। 
সবচেয়ে L.H.S টা হবে
$ \sqrt{\frac{x_{1}^{2}+x_{2}^{2}+\cdot \cdot \cdot +x_{n}^{2}}{n}}$
ওহ না, এডিট করে ফেলছি।কিন্তু এখন এই পোস্ট টা ডিলিট করা যাচ্ছে নাহ।
সবচেয়ে L.H.S টা হবে
$ \sqrt{\frac{x_{1}^{2}+x_{2}^{2}+\cdot \cdot \cdot +x_{n}^{2}}{n}}$
ওহ না, এডিট করে ফেলছি।কিন্তু এখন এই পোস্ট টা ডিলিট করা যাচ্ছে নাহ।
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Re: inequality of means (bomc)
অন্তত একটা রিপ্লাই না হলে মনে হয় remove করা যায় না। এবার চেষ্টা করে দেখতে পার।
হার জিত চিরদিন থাকবেই
তবুও এগিয়ে যেতে হবে.........
বাধা-বিঘ্ন না পেরিয়ে
বড় হয়েছে কে কবে.........
তবুও এগিয়ে যেতে হবে.........
বাধা-বিঘ্ন না পেরিয়ে
বড় হয়েছে কে কবে.........
Re: inequality of means (bomc)
What is AM GM QM HM??
Re: inequality of means (bomc)
What is AM GM QM HM??
-
nafistiham
- Posts:829
- Joined:Mon Oct 17, 2011 3:56 pm
- Location:24.758613,90.400161
- Contact:
Re: inequality of means (bomc)
actually,the rules are such 
or go here http://www.matholympiad.org.bd/forum/vi ... p?f=25&t=6Posting permissions:
1. Regular users can post messages and create polls in any forum, and reply any topic.
2. Remember Regular users can delete their post within 05 minutes starting from the posting time.
However, if someone replies you CAN NOT delete the post.
3. Regular users can edit a post within 2 days (48 hours) starting from the posting time
4. If you need to delete or edit the posts after the aforementioned time, please contact the administrator.
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.