$\displaystyle\sum{\frac1{a_n}}$, e.g. $$\frac 1 1 + \frac 1 2 + \frac 1 3 + \frac 1 4 + \dots + \frac 1 n$$ or
$$\frac 1 2 + \frac 1 4 + \frac 1 6 + \frac 1 8 + \dots + \frac 1 {2n}$$
What kind of series is this, and how do I sum it?
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sequences-and-series