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Lebl-Basic-Analysis-I
· Problem 2.6.13
Sequences and Series
Mathematics · series-convergence
Problem
Find a series
∑
n
=
1
∞
x
n
\sum_{n=1}^{\infty} x_n
∑
n
=
1
∞
x
n
that converges, but
∑
n
=
1
∞
x
n
2
\sum_{n=1}^{\infty} x_n^2
∑
n
=
1
∞
x
n
2
diverges. Hint: Compare Exercise 2.5.14.
Related theory
Series Convergence Tests And Absolute Convergence
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