All Questions
4
questions
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Is this summation equality true
A double factorial is such that $(2n)!!=(2n)(2n-2)...(2),$ and $(2n-1)!!=(2n-1)(2n-3)...3$. So $8!!=(8)(6)(4)(2)$. More information here: https://en.wikipedia.org/wiki/Double_factorial
With this in ...
- 79
1
vote
1
answer
69
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Determine if the series representation is true or not
A double factorial is such that $(2n)!!=(2n)(2n-2)...(2),$ and $(2n-1)!!=(2n-1)(2n-3)...3$. So $8!!=(8)(6)(4)(2)$. More information here: https://en.wikipedia.org/wiki/Double_factorial
With this in ...
- 79
0
votes
4
answers
74
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Show that $\sum_{n=1}^{\infty} nx^n/(n-1)! = e^xx(x+1)$
Please excuse my relatively novice skills, I'm first year (of 5) on my masters in mathematics.
I'm trying to show that
$$
\sum_{n=1}^{\infty} \frac{nx^n}{(n-1)!} = e^xx(x+1), \forall x.
$$
I already ...
- 19
1
vote
2
answers
196
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Closed-form summation of $\sum_{i=1}^n i\frac{x^i}{i!}$
Is there any way to find the closed-form of this finite summation, knowing that x<1? It is part of a larger equation that I am trying to solve/simplify, which has proven to use a lot of theory that ...
