For all `ngeq1`, prove that `1/(1. 2)+1/(2. 3)+1/(3. 4)+.....+1/(n(n+1))=n/(n+1)`

Explanation

To prove the statement

\[ \frac{1}{1 \cdot 2} + \frac{1}{2 \cdot 3} + \frac{1}{3 \cdot 4} + \ldots + \frac{1}{n(n+1)} = \frac{n}{n+1} \]

for all \( n \geq 1 \) using the principle of mathematical induction, we will follow these steps:

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