blade123 said: At n=o, you get Mo

At n=1, you get Mo+Mo/2 or 3Mo/2

blade123 said: If the second generation is 60% scale replicas. It would be 100% + 2*60% or 220%

blade123 said: I don't understand why they put the 2^n in the denominator and outside of the fraction, wouldn't it just simplify to Mo/(n+1)

Dschumanji said: It was most likely to make the infinite series look more complicated. Most people would not be able to easily recognize it in the second that it was flashed (I know I didn't recognize it). I think by doing this it is supposed to make the audience feel exactly like Fry.

I'm note sure where you are getting these terms, or perhaps I am not understanding what they represent. Can you explain your thinking, please?Again, mass doesn't scale in that fashion. Mass is directly proportional to theof the scale. To make things a bit simpler, suppose that you have a 1 kg cube with uniform density that measures 1 m on a side. If we scale the cube by 60%, we get a new cube that measures 0.6 units on a side. Mass is density times volume, and the volume of a cube is the cube of the side length. Thus the mass of the smaller cube is [itex](0.6{\rm\ m})^3\cdot 1\ {\rm kg}/{\rm m}^3 = 0.216\ {\rm kg}[/itex]. Thus in the second generation, there is one full-sized Bender that masses 100%, and two mini-Benders which mass 21.6% each, for a total of 143.2% the mass of the original Bender.I assume that this has something to do with how the formula was generated. Every term of the sum should basically have two terms: the number of mini-Benders in a particular generation, and the mass of each of those mini-Benders.The [itex]2^n[/itex] in the numerator is the number of mini-Benders in generation [itex]n[/itex]. This implies that [itex]\frac{m_0}{2^n(n+1)}[/itex] is meant to represent the mass of each of the mini-Benders in generation [itex]n[/itex]. This is the term that I am having trouble understanding.As to the [itex]2^n[/itex] in the numerator and denominator canceling---yes, they do cancel each other out, at which point we easily see that the remaining series is the mass of the original Bender times the harmonic series (which diverges). The animators or writers of Futurama probably left the terms in to make the sum look more complicated, or for some other aesthetic reason.Because most of their viewers would instantly recognize [itex]\sum_{n=0}^\infty \frac{m_0}{n+1}[/itex] as a harmonic series. :PThat being said, I clearly agree with your reasoning.xander