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Lebl-Basic-Analysis-I
· Problem 2.5.8
Sequences and Series
Mathematics · alternating-series
Problem
Show that
∑
n
=
1
∞
(
−
1
)
n
n
\displaystyle\sum_{n=1}^{\infty} \frac{(-1)^n}{n}
n
=
1
∑
∞
n
(
−
1
)
n
converges. Hint: Consider the sum of two subsequent entries.
Related theory
The Alternating Series Test
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