# set of number separated to convergent and divergent series

$${{..., -\frac{1}4,-\frac{1}3,-\frac{1}2, \frac{1}2,\frac{1}3,\frac{1}4... }}$$

Ok so i have to plot these things into series that is convergence and divergent that goes to infinity. all numbers are used but could that order could be changed.

I dont know where to start. Can anyone guide me thanks.

Im guessing you need to find the common factor but it said i have to use partial sums.

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ok im thinking you have to separate this into two series. one positive and one negative. ill let you guys know my progress –  user1730308 Jan 28 '13 at 3:38
Parsing through what you might mean, I assume it's to use these numbers, put them as elements of an ininite series such that the series converges/diverges. For convergence, label them like this: 1/2, -1/2, 1/3, -1/3, ... (limit 0); for divergence to $\infty$, note RHS goes to $\infty$ (as does LHS in absolute value) - take the first $n$ of RHS such that their sum is bigger than one, subtract first from LHS, add again the next $m$ elements of RHS s.t the sum is larger than 2, subtract 2nd of LHS, etc. You can achieve convergence to any number with this set of of numbers as series elements. –  gnometorule Jan 28 '13 at 4:09