Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
For
a
∈
R
a \in \mathbb{R}
a
∈
R
,
a
≠
−
1
a \neq -1
a
=
−
1
,
lim
n
→
∞
(
1
n
+
2
n
+
⋯
+
n
n
)
(
n
+
1
)
n
−
1
[
(
n
a
+
1
)
+
(
n
a
+
2
)
+
⋯
+
(
n
a
+
n
)
]
=
1
60
.
\lim_{n \to \infty} \frac{(1^n + 2^n + \dots + n^n)}{(n+1)^{n-1}\,[(na+1) + (na+2) + \dots + (na+n)]} = \frac{1}{60}.
n
→
∞
lim
(
n
+
1
)
n
−
1
[(
na
+
1
)
+
(
na
+
2
)
+
⋯
+
(
na
+
n
)]
(
1
n
+
2
n
+
⋯
+
n
n
)
=
60
1
.
Find
a
a
a
. a. 5 b. 7 c.
−
15
2
-\frac{15}{2}
−
2
15
d.
−
17
2
-\frac{17}{2}
−
2
17
Browse the problem library