Word Count : 342

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We are given the inequality: \[ 1 + \frac{1}{\sqrt{2}} + \cdots + \frac{1}{\sqrt{n}} > 2\sqrt{n+1} - 2 \quad \forall n \in \mathbb{N}. \] To solve this numerically, let's compute both the left-hand side (LHS) and the right-hand side (RHS) for a few values of \( n \). ### Step-by-step Calculation: 1. For \( n = 1 \): ___ _______ _______ ______ ______ ______ __________ ______ ________.
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