Moskie

hehe, this might be fun, i haven't done calc in forever, but i'll give it a try.

The way I'm starting this out is:

let r(n) be the radii of the (hemi)spheres. So r(1)=1, as defined in the problem. And r(n) < r(n-1). Now we have to show that the summation of all r's has a maximum value of 1+n^(1/2).

Does that sound right?

**edit** Found a stupid error in my logic. We don't just sum up the value of the radii, it's more complicated than that.... *continues scribbling*

ok, so who can figure out this part: if one hemisphere is stacked whose radius is x less than the sphere, how much height is added to the stack?

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Greetings and salutations.