Statement-1: For every natural number `nge2`,
`(1)/(sqrt(1))+(1)/(sqrt(2))+(1)/(sqrt(3))+...+(1)/(sqrt(n))gtsqrt(n)`
Statement-2: For every natural number `nge2,`
`sqrt(n(n+1))ltn+1`

Options

A. Statement-1 is true , Statement-2 is true, Statement-2 is correct explanation for Statement-1
B. Statement-1 is true , Statement-2 is true , Statement-2 is not a correct explanation for Statement-1
C. Statement-1 is true , Statement-2 is false
D. Statement-1 is false , Statement -2 is true .

Explanation

To solve the problem, we will use the principle of mathematical induction to prove Statement-1 and then analyze Statement-2.

### Step-by-Step Solution

**Step 1: Base Case (n = 2)**
We need to check if the statement holds for the base case, n = 2.
The left-hand side (LHS) is:
\[
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