I have what I assume is a very basic question on Ohm's law. Let's say that we have $n$ equal light bulbs in a series with a battery. We know that $$ U - IR - IR - \cdots -IR= U - nIR = 0.$$ Solving for the current gives $$I = \frac{U}{nR}.$$ From Ohm's law we know that $$P = RI^{2}=\frac{U^2}{nR},$$ but we also know Ohm's law can be written as $$P=UI=\frac{U^2}{nR},$$ but that does not give the same answer as the other expression. Why don't they give the same answer?
What am I missing?
The original question is from this exam that I found on the Internet. It is question 1a). http://aesop.phys.utk.edu/ph231/fin.pdf and solution can be found here http://aesop.phys.utk.edu/ph231/fins.pdf