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Lebl-Basic-Analysis-I
· Problem 2.5.4
Sequences and Series
Mathematics · series-convergence-divergence
Problem
a) Prove that if
∑
n
=
1
∞
x
n
\sum_{n=1}^{\infty} x_n
∑
n
=
1
∞
x
n
converges, then
∑
n
=
1
∞
(
x
2
n
+
x
2
n
+
1
)
\sum_{n=1}^{\infty} (x_{2n} + x_{2n+1})
∑
n
=
1
∞
(
x
2
n
+
x
2
n
+
1
)
also converges. b) Find an explicit example where the converse does not hold.
Related theory
Series Convergence Tests And Absolute Convergence
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