Prove by the principle of mathematical induction that for all `n N :\ ` `1/(1. 3)+1/(35)+1/(57)++1/((2n-1)(2n+1))=n/(2n+1)`

Explanation

To prove the statement

\[ \frac{1}{(1)(3)} + \frac{1}{(3)(5)} + \frac{1}{(5)(7)} + \ldots + \frac{1}{(2n-1)(2n+1)} = \frac{n}{2n+1} \]

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

...