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.
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.
Proof of geometric series formula Ask Question Asked 4 years, 7 months ago Modified 4 years, 7 months ago
The geometric mean is a useful concept when dealing with positive data. But for negative data, it stops being useful. Even in the cases where it is defined (in the real numbers), it is no longer guaranteed to give a useful response. Consider the "geometric mean" of $-1$ and $-4$. Your knee-jerk formula of $\sqrt { (-1) (-4)} = 2$ gives you a result that is obviously well removed from the ...
- 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?
On Wikipedia, the terms Exponential Growth and Geometric Growth are listed as synonymous, and defined as when the growth rate of the value of a mathematical function is proportional to the function's