+0

# Let . Evaluate(This sum has 1000 terms, one for the result when we input each integer from 1 to 1000 into .)

0
716
1

Let . Evaluate(This sum has 1000 terms, one for the result when we input each integer from 1 to 1000 into .)

Guest Jan 8, 2015

#1
+80865
+10

floor [ (2-3x) / (x + 5) ]

This isn't as daunting as it seems

Notice the first few terms....

f(1) = floor( -1 /6) = -1   ..   f(2) = floor (-4/7) = -1... f(3) = floor (-7/8) = -1  ...f(4) = floor (-10/9)= -2

And f(11)  = floor (-31/16) = -2   ....and f(12) = floor (-34 / 17) = -2 and f(13) =floor (-37/18) = -3

And every successive term has has a floor of -3....for example f(1000) = floor(-2998/ 1005) = -3

So.... 3 terms have a floor = -1

And 9 terms have a floor of -2

And (1000 - 12) = (988) terms have a floor of -3

So the sum is   3(-1) + 9(-2) + 988(-3)  = -2985

CPhill  Jan 8, 2015
Sort:

#1
+80865
+10

floor [ (2-3x) / (x + 5) ]

This isn't as daunting as it seems

Notice the first few terms....

f(1) = floor( -1 /6) = -1   ..   f(2) = floor (-4/7) = -1... f(3) = floor (-7/8) = -1  ...f(4) = floor (-10/9)= -2

And f(11)  = floor (-31/16) = -2   ....and f(12) = floor (-34 / 17) = -2 and f(13) =floor (-37/18) = -3

And every successive term has has a floor of -3....for example f(1000) = floor(-2998/ 1005) = -3

So.... 3 terms have a floor = -1

And 9 terms have a floor of -2

And (1000 - 12) = (988) terms have a floor of -3

So the sum is   3(-1) + 9(-2) + 988(-3)  = -2985

CPhill  Jan 8, 2015

### 20 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details