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Mathematics
Problem
State the condition on the limit
L
=
lim
n
→
∞
∣
a
n
+
1
a
n
∣
L=\displaystyle\lim_{n\to\infty}\left|\frac{a_{n+1}}{a_n}\right|
L
=
n
→
∞
lim
a
n
a
n
+
1
that guarantees convergence of the series
∑
a
n
\sum a_n
∑
a
n
under the ratio test.
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