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Mathematics
Problem
Let
S
1
(
n
)
=
∑
k
=
1
n
k
S_1(n)=\sum_{k=1}^{n} k
S
1
(
n
)
=
∑
k
=
1
n
k
,
S
2
(
n
)
=
∑
k
=
1
n
k
2
S_2(n)=\sum_{k=1}^{n} k^{2}
S
2
(
n
)
=
∑
k
=
1
n
k
2
and
S
3
(
n
)
=
∑
k
=
1
n
k
3
S_3(n)=\sum_{k=1}^{n} k^{3}
S
3
(
n
)
=
∑
k
=
1
n
k
3
. As
n
n
n
becomes very large, which sum grows the fastest? a)
S
2
(
n
)
S_2(n)
S
2
(
n
)
b)
S
3
(
n
)
S_3(n)
S
3
(
n
)
c) All three grow at the same rate d)
S
1
(
n
)
S_1(n)
S
1
(
n
)
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