Using the principle of mathematical induction prove that `1/(1. 2. 3)+1/(2. 3. 4)+1/(3. 4. 5)++1/(n(n+1)(n+2))=(n(n+3))/(4(n+1)(n+2)` for all `n in N`

Explanation

To prove the statement

\[ \sum_{k=1}^{n} \frac{1}{k(k+1)(k+2)} = \frac{n(n+3)}{4(n+1)(n+2)} \]

for all \( n \in \mathbb{N} \) using the principle of mathematical induction, we will follow these steps:

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