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Mathematics
Mathematics
Problem
Give a brief justification for the identity
(
n
k
)
+
(
n
k
+
1
)
=
(
n
+
1
k
+
1
)
\displaystyle {n\choose k}+{n\choose k+1}={n+1\choose k+1}
(
k
n
)
+
(
k
+
1
n
)
=
(
k
+
1
n
+
1
)
, where
n
n
n
and
k
k
k
are positive integers with
0
≤
k
≤
n
−
1
0\le k\le n-1
0
≤
k
≤
n
−
1
.
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