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Let \(f(x) = \left\lfloor\dfrac{2 - 3x}{x + 5}\right\rfloor\). Evaluate \(f(1)+f(2) + f(3) + \cdots + f(999)+f(1000).\) This sum has 1000 terms, one for the result when we input each integer from 1 to 1000 into f.

 Apr 16, 2020
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Every term is -2, so the sum is -2000.

 Apr 16, 2020

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