- #1
Mr Davis 97
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Homework Statement
Suppose that ##a_n## is a sequence such that ##\sum_{n=1}^\infty a_n^2## converges. Show that ##\lim_{n\to\infty}a_n = 0##.
Homework Equations
The Attempt at a Solution
My idea was this. Since ##a_n^2## converges, we have that ##\lim_{n\to\infty}a_n^2 = 0##. I want to claim that ##\lim_{n\to\infty}a_n^2 = (\lim_{n\to\infty}a_n)^2 = 0##, but is this justified? Don't I have to know that ##a_n## does in fact converge before I can use the algebra of limits?