Question

(absolute value of a series)
Is this correct:

Answer 1

\[\sum_{n=1}^{\infty} \left| \frac{ (-1)^n }{ n} \right| = \left| \frac{ (-1)^1 }{ 1} \right| + \left| \frac{ (-1)^2 }{ 2} \right| + \left| \frac{ (-1)^3 }{ 3} \right| ...\]

Answer 2

Looks correct. You can of course simplify (-1)^2 so the term becomes 1/2.

Answer 3

but the abs value carries in this way, as apposed to surrounding the entire partial sum?