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 ?

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- February 20th 2010, 09:14 AMcoobeWhy does this converge ?

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 ? - February 20th 2010, 09:20 AMDrexel28
- February 20th 2010, 11:52 AMshayan603
1/k does not diverge to infinity, it converges to 0

- February 20th 2010, 11:53 AMDrexel28
- February 20th 2010, 12:04 PMcoobe
so the harmonic series does diverge while the alternating harmonic series converge ?

- February 20th 2010, 12:05 PMDrexel28