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Question 6

If $$\frac{1}{1 \times 2} + \frac{1}{2 \times 3} + \ldots + \frac{1}{n \times (n+1)} = \frac{19}{20}$$ then $$n =$$

Solution

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The sum telescopes to $$1 - \frac{1}{n+1} = \frac{n}{n+1}$$. Setting $$\frac{n}{n+1} = \frac{19}{20}$$ gives $$n = 19$$.

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