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.

Proof of the Law of Large Numbers Part 1: The Weak Law, by Andrew Rothman

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probability - Which Law of Large Numbers ensures the second equation in the picture is true? - Mathematics Stack Exchange

Why would the law of large numbers work if every event is completely independent? - Quora

The Joy Of X: A Guided Tour of Math, from One to Infinity: Strogatz, Steven: 2015544105850: : Books

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

Week 121 Law of Large Numbers Toss a coin n times. Suppose X i 's are Bernoulli random variables with p = ½ and E(X i ) = ½. The proportion of

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probability - Weak law vs strong law of large numbers - intuition - Cross Validated

real analysis - Strong Law of Large Numbers - Converse - Mathematics Stack Exchange