MathDB
Problems
Contests
Undergraduate contests
Putnam
2002 Putnam
1
Putnam 2002 A1
Putnam 2002 A1
Source:
March 12, 2012
Putnam
calculus
derivative
function
limit
college contests
Problem Statement
Let
k
k
k
be a fixed positive integer. The
n
n
n
th derivative of
1
x
k
−
1
\tfrac{1}{x^k-1}
x
k
−
1
1
has the form
P
n
(
x
)
(
x
k
−
1
)
n
+
1
\tfrac{P_n(x)}{(x^k-1)^{n+1}}
(
x
k
−
1
)
n
+
1
P
n
(
x
)
, where
P
n
(
x
)
P_n(x)
P
n
(
x
)
is a polynomial. Find
P
n
(
1
)
P_n(1)
P
n
(
1
)
.
Back to Problems
View on AoPS