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Mathematics
Problem
Prove that for any non-negative integers
n
n
n
and
r
r
r
,
∑
k
=
0
r
(
n
+
k
k
)
=
(
n
+
r
+
1
r
+
1
)
.
\sum_{k=0}^{r}{\,n+k\choose k}={n+r+1\choose r+1}.
k
=
0
∑
r
(
k
n
+
k
)
=
(
r
+
1
n
+
r
+
1
)
.
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