Again, shattered by this question on series, I did have no clue how to begin. Sequences limits are approached through absolute values of the $n$-th term and the assumed limit being smaller than a given delta. And this for a given $N$. I don't see the link with power-series exercises, as for an example, the following:
Find a $K$, such that for all $n \geq K$ we have $\frac{1}{\sqrt1} + \frac{1}{\sqrt2} + \ldots + \frac{1}{\sqrt{n}} > 1000$
Help me with this one to, but more interesting is, how the theory on sequences applies to these problems. Or don't they?