Use induction to show that for all `n in N`.
`sqrt(a+sqrt(a+sqrt(a+....+sqrt(a))))lt (1+sqrt((4a+1)))/(2)`
where'a' is fixed positive number and n radical signs are taken on LHS.

Explanation

To prove the statement using mathematical induction, we will follow the standard steps of induction: the base case, the induction hypothesis, and the induction step.

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

Let \( P(1) \) be the statement:
\[
\sqrt{a} < \frac{1 + \sqrt{4a + 1}}{2}
...