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Mathematics
Problem
Consider the two sums
S
1
=
∑
k
=
1
n
(
4
k
+
2
)
S_1 = \displaystyle \sum_{k=1}^{n}(4k+2)
S
1
=
k
=
1
∑
n
(
4
k
+
2
)
and
S
2
=
∑
k
=
0
n
−
1
(
4
k
+
2
)
S_2 = \displaystyle \sum_{k=0}^{n-1}(4k+2)
S
2
=
k
=
0
∑
n
−
1
(
4
k
+
2
)
. Are
S
1
S_1
S
1
and
S
2
S_2
S
2
equal for the same positive integer
n
n
n
? Give a brief reason for your answer.
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