Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Problem
Problem
The value of
lim
n
→
∞
∑
K
=
1
n
n
−
K
n
2
cos
(
4
K
n
)
\lim_{n \to \infty} \sum_{K=1}^{n} \frac{n-K}{n^2} \cos \left( \frac{4K}{n} \right)
lim
n
→
∞
∑
K
=
1
n
n
2
n
−
K
cos
(
n
4
K
)
equals a.
1
4
sin
4
+
1
16
cos
4
−
1
16
\frac{1}{4} \sin 4 + \frac{1}{16} \cos 4 - \frac{1}{16}
4
1
sin
4
+
16
1
cos
4
−
16
1
b.
1
4
sin
4
−
1
16
cos
4
+
1
16
\frac{1}{4} \sin 4 - \frac{1}{16} \cos 4 + \frac{1}{16}
4
1
sin
4
−
16
1
cos
4
+
16
1
c.
1
16
(
1
−
sin
4
)
\frac{1}{16} (1 - \sin 4)
16
1
(
1
−
sin
4
)
d.
1
16
(
1
−
cos
4
)
\frac{1}{16} (1 - \cos 4)
16
1
(
1
−
cos
4
)
Browse the problem library