Prove the following by using the principle of mathematical induction for all `n in N`:`1/(2. 5)+1/(5. 8)+1/(8. 11)+...+1/((3n-1)(3n+2))=n/((6n+4))`

Explanation

To prove the statement

\[ \frac{1}{(2 \cdot 5)} + \frac{1}{(5 \cdot 8)} + \frac{1}{(8 \cdot 11)} + \ldots + \frac{1}{((3n-1)(3n+2))} = \frac{n}{(6n+4)} \]

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

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