Prove the following by using the principle of mathematical induction for all `n in N`:`1/(1. 4)+1/(4. 7)+1/(7. 10)+...+1/((3n-1)(3n+1))=n/((3n+1))`.

Explanation

To prove the statement

\[ \frac{1}{(1 \cdot 4)} + \frac{1}{(4 \cdot 7)} + \frac{1}{(7 \cdot 10)} + \ldots + \frac{1}{((3n-1)(3n+1))} = \frac{n}{(3n+1)} \]

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

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