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Let f(x) = lfloor (2 - 3x)/(3x + 8) \rfloor
Evaluate $f(1)+f(2) + f(3) + \dots + f(999)+f(1000).$ (This sum has $1000$ terms, one for the result when we input each integer from $1$ to $1000$ into $f$.)

 Dec 28, 2024
 #1
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Each term   will  be -1 < term value  < 0

 

So the floor for each will be -1

 

Sum = 1000 (-1)  = -1000

 

 

cool cool cool

 Dec 28, 2024

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