Proof of geometric series formula Ask Question Asked 4 years, 7 months ago Modified 4 years, 7 months ago
- 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
3 A clever solution to find the expected value of a geometric r.v. is those employed in this video lecture of the MITx course "Introduction to Probability: Part 1 - The Fundamentals" (by the way, an extremely enjoyable course) and based on (a) the memoryless property of the geometric r.v. and (b) the total expectation theorem.
$$\det(A^T) = \det(A)$$ Using the geometric definition of the determinant as the area spanned by the columns, could someone give a geometric interpretation of the property?
I'm not familiar with the equation input method, so I handwrite the proof. I'm using the variant of geometric distribution the same as @ndrizza. Therefore E [X]=1/p in this case. handwritten proof here
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