Let \(f(x) = x - \lfloor \sqrt{x} \rfloor^2\). What is \(f(101) + f(102) + f(103) + \cdots + f(110)?\)
+14995 Let \(f(x) = x - \lfloor \sqrt{x} \rfloor^2 \) What is \(f(101) + f(102) + f(103) + \cdots + f(110)? \)
Hello Guest!
\(f(x) = x - \lfloor \sqrt{x} \rfloor^2 \)
\(f(101) + f(102) + f(103) + \cdots + f(110)=0 \)
!
+118677 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)
+118677 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.
