# What is Holder's Inequality? [closed]

I have done some research on the internet about the inequality called Holder, but I've encountered some explanations in sites like Turkis Math Wikipedia or Wolfram but none of those explanations were helpful enough, I want to be able to define what Holder's Inequality is and solve inequality questions using Holder's, I need an elementary level explanation, I do not know integrals, I am not very well informed about series (at least in some level), I am a Turkish high school student in preparation for Maths Olympiad, so I know about Cauchy-Schwarz, AM-GM and all these other concepts, if I am not advanced enough to understand the definition of it or put it to application, what topics should I study first?

Thank you:)

## closed as off-topic by GAVD, José Carlos Santos, Namaste, JMP, Xander HendersonSep 25 '17 at 1:33

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Anyway, this is Hölder's inequality, as I know it. Let $$p$$, $$q$$ be positive real numbers such that $$\frac{1}{p} + \frac{1}{q} = 1$$. Also, let $$a_1, \: \dots, \: a_n$$ and $$b_1, \: \dots, \: b_n$$ be nonnegative real numbers. Then $$\sum_{i = 1}^n a_ib_i \le \left(\sum_{i = 1}^n a_i^p\right)^{1/p} \left(\sum_{i = 1}^n b_i^q\right)^{1/q}$$