Maths Olympiad Prep

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Algebra Difficulty 4.6 AIME Find the answer

2. 12002+13.003−14004+16006−18008\frac{1}{2002}+\frac{1}{3.003}-\frac{1}{4004}+\frac{1}{6006}-\frac{1}{8008} =()=(\quad).

Pick one

Solution

Prompt: Transform the denominator of each fraction to
2×1001,3×1001,4×1001,6×1001,8×1001. \begin{array}{l} 2 \times 1001, 3 \times 1001, 4 \times 1001, \\ 6 \times 1001, 8 \times 1001 . \end{array}

Answer: 58008\frac{5}{8008}.

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.