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The first one is about series of positive terms like, for example [tex]\sum _{i=0}^{inf}(n^{1/n}-1)[/tex].

Can i say that as the square of this series of positive terms diverges by the "nth term test", the original series also diverges.

If i can't use this, could you please point me on the right direction in order to do determine the convergence of this series?.

My second question is about a limit by definition(lambda-epsilon proof). I have to find out if the following function is continuous and/or differentiable:

[tex]f(x,y) =\left\{\begin{array}{cc}\frac {x*y} {\sqrt x -\sqrt y},&\mbox{ if }x\neq y\\0, & \mbox{x=y}\end{array}\right[/tex]

Everything i tried indicates that this function is continuous, but i can't prove that the limit when (x,y)->(0,0) of f is in fact 0.

I you want me to explain a little better what i have done just ask. I would really appreciate any help you could give me.

Many Thanks, Paul.