## Online Course Discussion Forum

### MC-IV week 1 homework help

MC-IV week 1 homework help

Can someone give me a hint on problem #5? I used AM-GM on both sides and reached the same expression on both sides. I know I need to find something in middle but so far no luck.

Re: MC-IV week 1 homework help

Have you tried Rearrangement Inequality?

Note: the problem in question is the following:

Let $a_i>0 (i=1,2,\ldots,n)$, and real numbers $x,y$ satisfy $xy>0$. Show
$$\frac{a_1^x}{a_2^y}+\frac{a_2^x}{a_3^y}+\cdots+\frac{a_{n-1}^x}{a_n^y}+\frac{a_n^x}{a_1^y} \geq \sum_{i=1}^n a_i^{x-y}.$$

(Edited by Areteem Institute based on comment from William Chen- original submission Friday, June 15, 2018, 11:56 PM)

Re: MC-IV week 1 homework help

Is there a typo in the problem? I think the right hand side should be

Should $\sum_{i=1}^n a_n^{x-y}$ be $\sum_{i=1}^n a_i^{x-y}$