probability - Condition for strong law of large numbers : Understanding the solution - Mathematics Stack Exchange

I am reading the solution of the following task: Here is the solution: From where does the last inequality in the second line comes from? Everything else is totally clear to me.

Law of Large Numbers - Probability

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probability - Proof explanation - weak law of large numbers - Mathematics Stack Exchange

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probability theory - Strong Law of Large Numbers (Klenke's proof) - Mathematics Stack Exchange

Proof of the Law of Large Numbers Part 2: The Strong Law, by Andrew Rothman