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Lebl-Basic-Analysis-I
· Problem 2.5.14
Sequences and Series
Mathematics · series-convergence
Problem
Suppose
∑
n
=
1
∞
x
n
\sum_{n=1}^{\infty} x_n
∑
n
=
1
∞
x
n
converges and
x
n
≥
0
x_n \geq 0
x
n
≥
0
for all
n
n
n
. Prove that
∑
n
=
1
∞
x
n
2
\sum_{n=1}^{\infty} x_n^2
∑
n
=
1
∞
x
n
2
converges.
Related theory
Series Convergence Tests And Absolute Convergence
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