# Thread: Why does this converge ?

1. ## Why does this converge ?

$\sum (-1)^{k+1} * \frac {1} {k}$

k starts at 1 and sum goes to infinity

since 1/k is diverging and its limit is infinity, why does the series converge ? isnt it necessary for an alternating series to go strictly to 0 as k approaches infinity to be a convergent series ?

2. Originally Posted by coobe
$\sum (-1)^{k+1} * \frac {1} {k}$

k starts at 1 and sum goes to infinity

since 1/k is diverging and its limit is infinity, why does the series converge ? isnt it necessary for an alternating series to go strictly to 0 as k approaches infinity to be a convergent series ?

3. 1/k does not diverge to infinity, it converges to 0

4. Originally Posted by shayan603
1/k does not diverge to infinity, it converges to 0
He obviously meant the harmonic series.

5. so the harmonic series does diverge while the alternating harmonic series converge ?

6. Originally Posted by coobe
so the harmonic series does diverge while the alternating harmonic series converge ?
True dat.