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

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1. JuanPerez

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

2. pasta

i think yes . and i do not require the "if" to see it.The results will always be <infinity

3. 2le

$\sum_{n}^{k}na_n^2=\sum_{n}^{k}n*\sum_{n}^{k}a_n*\sum_{n}^{k}a_n<\infty$ Since the larger of the 3 summations is less than infinity, that would also make the individual summation less than infinity as well.