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\[\sum_{0}^{infinity}(\sqrt(k+1) -\sqrt(k))/k\]

wait does it converge to 0 if it is so....i can give you an explanation

The starting index should probably be 1.

Oh yeah, starting index is 1 my bad

yeah,, parth is right

\[\large \sum_{k=1}^{\infty} \left(\frac{\sqrt{k+1} -\sqrt{k}}{k}\right)\]

\[\sqrt{k-1/k} -1\]
\[\sqrt{1-1/k} -1\]
if k goes to infinity
1/k goes to zero
then
\[\sqrt{1}-1=0\]

but you've got to show the convergence of the series

Yeah, it's not enough to show the sequence goes to 0, otherwise 1/n would converge.

Unless I'm missing something about what you're saying.

Could you perhaps use a ratio test to show convergence?

i think i should that on ... do i have to use the summation sign?

oh wait... i got what ur saying now

\[\lim_{k\rightarrow \infty} \sqrt[n]{|a_n|} \ne 1\] The root test might work too.

whoop, meant o write n instead of k*

Oh right didn't think of the root test. That might work out more nicely.

So you'd end up with some k^(k+1/2) type stuff, all of which would go to 1 right?

Is that right?