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- Proof of geometric series formula - Mathematics Stack Exchange
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- statistics - What are differences between Geometric, Logarithmic and . . .
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
- why geometric multiplicity is bounded by algebraic multiplicity?
The geometric multiplicity the be the dimension of the eigenspace associated with the eigenvalue $\lambda_i$ For example: $\begin{bmatrix}1 1\\0 1\end{bmatrix}$ has root $1$ with algebraic multiplicity $2$, but the geometric multiplicity $1$ My Question: Why is the geometric multiplicity always bounded by algebraic multiplicity? Thanks
- What does the dot product of two vectors represent?
It might help to think of multiplication of real numbers in a more geometric fashion $2$ times $3$ is the length of the interval you get starting with an interval of length $3$ and then stretching the line by a factor of $2$ For dot product, in addition to this stretching idea, you need another geometric idea, namely projection
- What is the difference between arithmetic and geometrical series?
Geometric and arithmetic are two names that are given to different sequences that follow a rather strict pattern for how one term follows from the one before An arithmetic sequence is characterised by the fact that every term is equal to the term before plus some fixed constant, called the difference of the sequence For instance, $$ 1,4,7,10
- Series expansion: $\frac{1}{(1-x)^n}$ - Mathematics Stack Exchange
I realize this is an old thread, but I wanted to expand on the above answers on how to derive the formula for anyone else that might come along Starting with the geometric series and taking successive derivatives:
- terminology - Is it more accurate to use the term Geometric Growth or . . .
In both geometric and exponential growth we find multiplication by a fixed factor The distinction lies in that 'exponential growth' is typically used to describe continuous time growth (steps of infinitesimal time) whilst geometric growth is used to describe discrete time growth (steps of unit time)
- Calculate expectation of a geometric random variable
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
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