MathDB
Problems
Contests
National and Regional Contests
China Contests
(China) National High School Mathematics League
2005 China Second Round Olympiad
3
3
Part of
2005 China Second Round Olympiad
Problems
(1)
summation
Source: 2005 China Second Round Olympiad
9/2/2014
For each positive integer, define a function
f
(
n
)
=
{
0
,
if n is the square of an integer
⌊
1
{
n
}
⌋
,
if n is not the square of an integer
.
f(n)=\begin{cases}0, &\text{if n is the square of an integer}\\ \\ \left\lfloor\frac{1}{\{\sqrt{n}\}}\right\rfloor, &\text{if n is not the square of an integer}\end{cases}.
f
(
n
)
=
⎩
⎨
⎧
0
,
⌊
{
n
}
1
⌋
,
if n is the square of an integer
if n is not the square of an integer
.
Find the value of
∑
k
=
1
200
f
(
k
)
\sum_{k=1}^{200} f(k)
∑
k
=
1
200
f
(
k
)
.
function
floor function
geometry
geometric transformation
algebra unsolved
algebra