MathDB
Problems
Contests
Undergraduate contests
Putnam
2020 Putnam
B6
B6
Part of
2020 Putnam
Problems
(1)
Putnam 2020 B6
Source: 81st William Lowell Putnam Competition
2/22/2021
Let
n
n
n
be a positive integer. Prove that
∑
k
=
1
n
(
−
1
)
⌊
k
(
2
−
1
)
⌋
≥
0.
\sum_{k=1}^n (-1)^{\lfloor k (\sqrt{2} - 1) \rfloor} \geq 0.
k
=
1
∑
n
(
−
1
)
⌊
k
(
2
−
1
)⌋
≥
0.
(As usual,
⌊
x
⌋
\lfloor x \rfloor
⌊
x
⌋
denotes the greatest integer less than or equal to
x
x
x
.)
Putnam
Putnam 2020