4 I think geometric interpretations can be quite helpful in solving some inequalities. There's quite a nice geometric proof for the Quadratic Mean - Arithmetic Mean - Geometric Mean - Harmonic Mean inequality. Some other inequalities such as Holder and Minkowski benefit from arguments about geometric convexity.
- does the proof above make sure that $a_n$ is not arithmetic? a sequence cannot be arithmetic and geometric at the same time, right? 2) what about more complex expressions? like $b_n=ln (n)$? how do I quickly see if it is arithmetic or geometric sequence?
Proof of geometric series formula Ask Question Asked 4 years, 6 months ago Modified 4 years, 6 months ago
For questions related to geometric programming, which considers problems that optimize a polynomial subject to polynomial and monomial constraints.
Now lets do it using the geometric method that is repeated multiplication, in this case we start with x goes from 0 to 5 and our sequence goes like this: 1, 2, 2 2=4, 2 2 2=8, 2 2 2 2=16, 2 2 2 2 2=32. The conflicts have made me more confused about the concept of a dfference between Geometric and exponential growth.
I was trying to derive the Negative Binomial Distribution from a Sum of Geometric Random Variables. I was attempting to do this without any MGF's and hopefully from basic summation and series properties if possible.
What is the geometric reasoning that leads us to understand that the dot product of $\mathbf {a}$ with this normal vector is equal to the volume of the parallelepiped defined by the three vectors? I would greatly appreciate it if people would please take the time to explain this.
Probabilities of random geometric objects having certain properties (enclosing the origin, having an acute angle,...); expected counts, areas, ... of random geometric objects. For questions about the geometric distribution, use the tag [probability-distributions] instead.