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

Explanation

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

### Step 1: Base Case
We need to check if the statement holds for \( n = 1 \).

**Left Hand Side (LHS)**:
\[
P(1) = 1
...