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MathNet 2019-part-04 — 184 problems (EN–VI) Question 42

Math Olympiad Vault · MathNet 2019-part-04 — 184 problems (EN–VI)

Question 42

Compute the limit
$$
\lim_{n \rightarrow \infty} \left( \left(1+\frac{1}{2}\right) \cdot \left(1+\frac{1}{2+3}\right) \cdot \ldots \cdot \left(1+\frac{1}{2+3+\ldots+n}\right) \right).
$$