# Inequality

#### MarkFL

Staff member
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.

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