Using principle of mathematical induction prove that `sqrtn<1/sqrt1+1/sqrt2+1/sqrt3+......+1/sqrtn` for all natural numbers `n >= 2`.

Explanation

To prove the statement \( \sqrt{n} < \frac{1}{\sqrt{1}} + \frac{1}{\sqrt{2}} + \frac{1}{\sqrt{3}} + \ldots + \frac{1}{\sqrt{n}} \) for all natural numbers \( n \geq 2 \) using the principle of mathematical induction, we will follow these steps:

### Step 1: Base Case
We start by checking the base case \( n = 2 \).

\[ \text{LHS: } \sqrt{2} \approx 1.414 \]
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