# Why does this converge ?

• Feb 20th 2010, 09:14 AM
coobe
Why does this converge ?
$\displaystyle \sum (-1)^{k+1} * \frac {1} {k}$

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 ?
• Feb 20th 2010, 09:20 AM
Drexel28
Quote:

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

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 ?

Wiki, your best firend
• Feb 20th 2010, 11:52 AM
shayan603
1/k does not diverge to infinity, it converges to 0
• Feb 20th 2010, 11:53 AM
Drexel28
Quote:

Originally Posted by shayan603
1/k does not diverge to infinity, it converges to 0

He obviously meant the harmonic series.
• Feb 20th 2010, 12:04 PM
coobe
so the harmonic series does diverge while the alternating harmonic series converge ?
• Feb 20th 2010, 12:05 PM
Drexel28
Quote:

Originally Posted by coobe
so the harmonic series does diverge while the alternating harmonic series converge ?

True dat.