If [\ sum n a^2_n < \infty \] is it true that [\ sum n a_n < \infty \]??

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If [\ sum n a^2_n < \infty \] is it true that [\ sum n a_n < \infty \]??

MIT 18.01 Single Variable Calculus (OCW)
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If \[\sum n a^2_n <\infty \]is it true that \[ \sum a_n < \infty \] ????
i think yes . and i do not require the "if" to see it.The results will always be
\[\sum_{n}^{k}na_n^2=\sum_{n}^{k}n*\sum_{n}^{k}a_n*\sum_{n}^{k}a_n<\infty\] Since the larger of the 3 summations is less than infinity, that would also make the individual summation less than infinity as well.

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