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Inequality

mathworker

Active member
May 31, 2013
118

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
Re: inequality

The actual problem statement here may be written as:

Given \(\displaystyle a_i>0\), \(\displaystyle \sum_{i=1}^n a_i=1\) and \(\displaystyle a_{n+1}=a_{1}\)

Prove:

\(\displaystyle \sum_{i=1}^{n}\dfrac{a_{i}}{a_{i+1}}\ge\sum_{i=1}^{n}\dfrac{1-a_{i+1}}{1-a_{i}}\)

Note: Normally, when a problem is posted in this sub-forum, the OP is expected to have a solution ready to post. However, the OP did not originally post the topic here and during a staff discussion, it was felt that this sub-forum would be best as it really does not fit into any neat category. So, consider this problem a challenge for our membership as a whole. (Cool)
 
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