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Mathematics
Problem
Explain why the series
∑
k
=
1
∞
a
k
\sum_{k=1}^{\infty} a_k
∑
k
=
1
∞
a
k
must diverge if
lim
n
→
∞
S
n
\lim_{n\to\infty} S_n
lim
n
→
∞
S
n
does not exist, where
S
n
=
∑
k
=
1
n
a
k
S_n=\sum_{k=1}^{n} a_k
S
n
=
∑
k
=
1
n
a
k
.
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