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1987 IMO Longlists
63
IMO LongList 1987 - Compute the sum
IMO LongList 1987 - Compute the sum
Source:
September 6, 2010
algebra unsolved
algebra
Problem Statement
Compute
∑
k
=
0
2
n
(
−
1
)
k
a
k
2
\sum_{k=0}^{2n} (-1)^k a_k^2
∑
k
=
0
2
n
(
−
1
)
k
a
k
2
where
a
k
a_k
a
k
are the coefficients in the expansion
(
1
−
2
x
+
x
2
)
n
=
∑
k
=
0
2
n
a
k
x
k
.
(1- \sqrt 2 x +x^2)^n =\sum_{k=0}^{2n} a_k x^k.
(
1
−
2
x
+
x
2
)
n
=
k
=
0
∑
2
n
a
k
x
k
.
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