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ਕਦਮ ਦਰ ਕਦਮ

1. \sum_{n=1}^{\infty} \frac{1}{n \left(n + 1\right)}

   Write the sum out.

2. \frac{1}{2} + \frac{1}{6} + \frac{1}{12} + \frac{1}{20} + \cdots

   The first few terms.

3. S_{3} \approx 0.75000, S_{6} \approx 0.85714, S_{11} \approx 0.91667, S_{51} \approx 0.98077

   Partial sums approach the limit.

4. = 1

   Infinite series: this converges, and the closed form is the limit of the partial sums.