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MathNet 1998 — Part 01 Question 92

Math Olympiad Vault · MathNet 1998 — Part 01

Question 92

Find the sum of the infinite series
$$
1 + 2\left(\frac{1}{1998}\right) + 3\left(\frac{1}{1998}\right)^{2} + 4\left(\frac{1}{1998}\right)^{3} + \ldots
$$