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Mathematics
Mathematics
Problem
Compare the growth of the three sums
∑
k
=
1
n
k
\displaystyle \sum_{k=1}^{n} k
k
=
1
∑
n
k
,
∑
k
=
1
n
k
2
\displaystyle \sum_{k=1}^{n} k^{2}
k
=
1
∑
n
k
2
and
∑
k
=
1
n
k
3
\displaystyle \sum_{k=1}^{n} k^{3}
k
=
1
∑
n
k
3
as
n
n
n
becomes very large. Which sum increases the fastest? State your answer with a brief reason.
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