Prove the following by using the principle of mathematical induction for all `n in N`:`1/(3. 5)+1/(5. 7)+1/(7. 9)+...+1/((2n+1)(2n+3))=n/(3(2n+3))`.

Explanation

To prove the statement

\[ \frac{1}{3 \cdot 5} + \frac{1}{5 \cdot 7} + \frac{1}{7 \cdot 9} + \ldots + \frac{1}{(2n+1)(2n+3)} = \frac{n}{3(2n+3)} \]

for all \( n \in \mathbb{N} \), we will use the principle of mathematical induction.

...