write 100 as a sum of numbers such that the product of those numbers is maximized. @Computer Science

Question

write 100 as a sum of numbers such that the product of those numbers is maximized.   @Computer Science

jamesj · Answer

How many numbers?

jamesj · Answer

2, 5, 10?  An arbitrary finite number?

anonymous · Answer

yes

anonymous · Answer

I got like $$\sum_{i=1}^{37}2.702702702702....$$

jamesj · Answer

That's right, because what you're doing is trying to maximize the function
$$ f(x) = x^{100/x} $$ subject to the constraint that 100/x is an integer.

Well if you differentiate that function and set it equal to zero, you'll find that f has a local max at x = e.  And as you can see, the x you have in your sum is very close to e.

anonymous · Answer

so it would be like $$\sum_{i=1}^{37}(2+702\sum_{n=1}^{\infty}{\frac{1}{10^{3n}}})$$

jamesj · Answer

But why bother with that?  All the intuitive content of the term is contained in the simple expression 100/37.

anonymous · Answer

right