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**HallsofIvy** Except that that last statement is untrue.

If it were true that those are divergent sequences whose sum was also a divergent sequence, that would prove nothing at all. In particular, it would not prove that "the sum of **any/** two divergent sequences. Plato suggested you look at those two sequences because they give a **counter-example**. In particular, $\displaystyle \lim_{n\to\infty}s_n+ t_n$ is NOT divergent. Actually write out four or five terms of the sequence and look at the sum $\displaystyle s_n+ t_n$.