so confused

Let  $f(x) = x - \lfloor \sqrt{x} \rfloor^2$ What is $f(101) + f(102) + f(103) + \cdots + f(110)?$

Hello Guest!

$f(x) = x - \lfloor \sqrt{x} \rfloor^2$

$f(101) + f(102) + f(103) + \cdots + f(110)=0$

  !

It is not going to be 0 because the floor of sqrtx is usually smaller than the sqrtx.

Have you tried to work this out yourself guest?

Show us what you have tried.

Hint: there is only 10 functions there. Just do them one by one.  Easy Peazy.   (I expect)

Perhaps you are unfamiliar with the floor function asinus.

$f(x) = x - \lfloor \sqrt{x} \rfloor^2\\ f(101)=101-\lfloor \sqrt{101} \rfloor^2=101-10^2=101-100=1 \\ f(102)=102-100=2\\ f(103)=3\\ ...\\ f(110)=10\\ $

So the sum is 1+2+3+...+10 = 1+10+2+9+3+8+4+7+5+6 = 11*5 = 55

I have not checked my answer carefully.