Problem 190 (difficulty: 2/10)

Is it true that if \(\displaystyle x_n\) is convergent, \(\displaystyle y_n\) is divergent then \(\displaystyle x_ny_n\) is divergent?

Solution:

No, for example \(\displaystyle x_n=\frac1{n^2}\) and \(\displaystyle y_n=n\).

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