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AIMO 2021 Primary 5 — Preliminary (Open Trial 1) Question 3

AIMO · AIMO 2021 Primary 5 — Preliminary (Open Trial 1)

Question 3

What is the sum of the first 1952 terms of the series $\frac11,\frac12,\frac22,\frac13,\frac23,\frac33,\frac14,\frac24,\frac34,\frac44,\ldots$?

Original choices: A: 1000; B: 1007,5; C: 1952; D: 1002.

Answer-format convention: Give the exact result as a short answer; the source choices are retained above.