All Questions
5
questions
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votes
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answers
39
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Converting a power series with recursively related coefficients into a single sigma sum expression
EDIT: Ok, silly me. There is an obvious closed form summation which somehow escaped me. Nonetheless, I would appreciate comments on deriving a characteristic polynomial from the generating function.
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- 434
1
vote
1
answer
300
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Proof that a sum is monotonically decreasing
This question is a follow up of the question asked in: Sum of a sequence which is neither arithmetic nor geometric
I have the following sum which doesn't seem to have a closed-form expression:
$$S_n =...
0
votes
1
answer
45
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Formula for weighed geometric sum
I'm trying to find an easy way to derive a formula for:
$S_{n} = \frac{1}{n}\sum_{i=0}^{n}(n-i)x^{i}$
I've found a recurrence relationship of sorts:
$S_{n+1} = \frac{xnS_{n}+n+1}{n+1} = x\frac{n}{n+...
- 125
3
votes
2
answers
144
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Summation of infinite series
If we know the series sum given below converges to a value $C$(constant)
$$\sum_{n=0}^{\infty}a_n =C \tag 2$$ Can we generate following in terms of C. values of $a_n$ will tend to zero as n goes to ...
- 1,717
0
votes
1
answer
39
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Summation of infinte series
Sir,
I have three infinite summation
$A =J_1 \sum_{n=2}^\infty (n-1) f(n-2) \tag 1$ , $B =\sum_{n=0}^\infty f(n) \tag 2$ and $C =J_2\sum_{n=1}^\infty f(n-1) \tag 3$, with $f(0)=2,f(1)...
- 1,717