- #1
Saladsamurai
- 3,020
- 7
Looking at the Harmonic series [tex]\sum_{k=1}^{\infty}\frac{1}{k}[/tex]
I at first justed accepted my teachers assertion that it diverges. I still do, not to mention that I trust my textbook (and Nicole Oresme!).
However in seems counterintuitive to me (and since it is math, I guess that is okay) .
It just seems that by virtue of the fact that [tex] \lim_{\k\rightarrow \infty}\frac{1}{k}=0[/tex] that at some point we would be adding zero to the sum.
Someone please help to clarify this.
Thanks,
Casey
p.s. I don't know why the "k" is not showing up under the limit sign:(
I at first justed accepted my teachers assertion that it diverges. I still do, not to mention that I trust my textbook (and Nicole Oresme!).
However in seems counterintuitive to me (and since it is math, I guess that is okay) .
It just seems that by virtue of the fact that [tex] \lim_{\k\rightarrow \infty}\frac{1}{k}=0[/tex] that at some point we would be adding zero to the sum.
Someone please help to clarify this.
Thanks,
Casey
p.s. I don't know why the "k" is not showing up under the limit sign:(