# Understand the problem

##### Source of the problem

##### Topic

##### Difficulty Level

##### Suggested Book

# Start with hints

Let us assume that . **Claim** works. Proof: For Trivial. For The inequality is equivalent to . Expanding, this becomes which is a consequence of . For Consider as a function of (say ). We need to show that the minimum of is at least 0. Clearly, is linear in and the coefficient of is . Due to the order chosen, this coefficient is non-negative. Hence the minimum is attained at the minimum of , which is . However, putting , we are left with which is true from the induction hypothesis. QED

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