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Mathematics
Mathematics
Problem
Show that for every positive integer
n
n
n
, the alternating sum of its binomial coefficients satisfies
∑
k
=
0
n
(
−
1
)
k
(
n
k
)
=
0.
\sum_{k=0}^{n}(-1)^k{n\choose k}=0.
k
=
0
∑
n
(
−
1
)
k
(
k
n
)
=
0.
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