+0  
 
0
12
1
avatar+952 

Let
f(x) = \left\lfloor\frac{3x - 5}{3x + 4}\right\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 $f$.)

 Apr 1, 2024
 #1
avatar+128794 
+1

f(1) =  -1

f(2) =   0

All   the other terms evaluate to 0   because the inside function will approach (but never reach) y = 1 since this is the horizontal  asymptote of that  function

 

So.....the sum  =  -1

 

cool cool cool

 Apr 1, 2024

2 Online Users

avatar