MHB What Is the Minimum Value of y in the Given Expression?

[juantheron]

If y = \mid x \mid+\mid x-1 \mid+\mid x-3 \mid+\mid x-6 \mid+...+\mid x-5151 \midand m = no. of terms in the expression yand n = no. of integers for which y has min. valueThen \displaystyle\frac{m+n-18}{10} =

 

[CaptainBlack]

If y = \mid x \mid+\mid x-1 \mid+\mid x-3 \mid+\mid x-6 \mid+...+\mid x-5151 \midand m = no. of terms in the expression yand n = no. of integers for which y has min. valueThen \displaystyle\frac{m+n-18}{10} =

Maybe it's me, but I find that incomprehensible.

For a start why is \(m\) not \(5152\)?

Do you mean \(n\) to be the number of integers corresponding to a local minima of \(y\)? You can show that there is a global minimum and it achived this at two adjacent integer points.

(the slope is -5152 for -ve \(x\), and increases by 2 when we pass a integer argument moving to the right ...)

CB