Prove the following by using induction for all `n in N`. `1+2+3+.....+n=(n(n+1))/(2)`

Explanation

To prove the statement \( P(n): 1 + 2 + 3 + \ldots + n = \frac{n(n+1)}{2} \) for all \( n \in \mathbb{N} \) using mathematical induction, we will follow these steps:

### Step 1: Base Case
We first check if the statement is true for \( n = 1 \).

**LHS:**
\[
1
...