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Contests
National and Regional Contests
Canada Contests
Canada National Olympiad
1997 Canada National Olympiad
5
5
Part of
1997 Canada National Olympiad
Problems
(1)
Evaluate Sum
Source: Canadian Mathematical Olympiad - 1997 - Problem 5.
5/7/2011
Write the sum
∑
i
=
0
n
(
−
1
)
i
⋅
(
n
i
)
i
3
+
9
i
2
+
26
i
+
24
\sum_{i=0}^{n}{\frac{(-1)^i\cdot\binom{n}{i}}{i^3 +9i^2 +26i +24}}
∑
i
=
0
n
i
3
+
9
i
2
+
26
i
+
24
(
−
1
)
i
⋅
(
i
n
)
as the ratio of two explicitly defined polynomials with integer coefficients.
ratio
algebra
polynomial
algebra unsolved