All Questions
13
questions with no upvoted or accepted answers
2
votes
0
answers
137
views
Can this summation be done without calculator?
Is it possible to perform the summation ,
$$\sum_{i=1}^{\infty} \frac{1}{i^i}$$
without the use of calculator?
It does converge to a finite value = 1.29129...
Wolfram Alpha link to this
Describe the ...
- 1,663
1
vote
0
answers
137
views
Simple algebra in rearring terms
I have a very simple mathematical question, and it is just about algebra which seems very tedious. First, let me state my problem from the beginning:
Let $i$ be an index representing countries ($i = {...
- 105
1
vote
0
answers
103
views
Restructuring Jacobi-Anger Expansion
In Jacobi-Anger expansion, $$e^{\iota z \sin(\theta)}$$ can be written as:
$$e^{\iota z \sin(\theta)} = \sum_{n=-\infty}^{\infty} J_n(z)e^{\iota n \theta}$$
where $J_n(z)$ is the Bessel function of ...
- 31
1
vote
0
answers
139
views
Solving a geometric-harmonic series
Find the value of $\displaystyle \frac21- \frac{2^3}{3^2}+ \frac{2^5}{5^2}- \frac{2^7}{7^2}+ \cdots$ till infinite terms.
found this problem while integrating $\arctan\left(x\right)/x$ from $0$ to $2$ ...
1
vote
0
answers
48
views
seperating two variables in a function with summation
I'm building a data analysis program that perform on big chunks of data, the issue I'm having is the speed of some operations; to be exact I have a function that takes two variables in this form : $$f(...
- 113
1
vote
0
answers
75
views
When is $a(n)$ prime?
Question: When is $a(n)\in P$ compared to all possible values of $n$? where $P$ denotes the set of primes. What is the density of the primes in the sequence?
Consider the sum of the prime counting ...
- 756
1
vote
1
answer
56
views
Given variable $m$, how do I find zeros of a polynomial in terms of $m$?
This is a summation question about a finite series with sum $m$. I'm trying to write a computer program that takes in a given integer $m$ (which represents the sum of a series) and outputs the number ...
- 11
0
votes
1
answer
38
views
How to simplify: $C_{t} = r[a_{t} + \frac{1}{1+r} * \sum_{j=0}^{\infty} (\frac{1}{1+r})^j * E(w_{t+j})]$
I have to find C_t (Optimal Consumption for each period). Thank you!
$$C_{t} = r[a_{t} + \frac{1}{1+r} * \sum_{j=0}^{\infty} (\frac{1}{1+r})^j * E(w_{t+j})]$$
Where,
$$w_{t+j} = \begin{cases} w + \...
0
votes
2
answers
49
views
Summation involving 2 variables
I am trying to understand how to expand a summation equation:
$$\sum_{j=1}^3 \sum_{i = j + 1}^4 (25-5i)$$
how do I expand the inner equation involving $i = j+1$ ?
Thanks!
- 1
0
votes
0
answers
52
views
Finding total of matrix, fraction with two variables
I'm trying to solve summation over a matrix that has been populated with an equation using two variables.
Trying to derive the a matrix populated with the equation:
$$f(x,y) = \frac{a}{x^2 + y - b}$...
- 53
0
votes
1
answer
72
views
A Finite Summation
Is there an easy way to find the following summation (question created by Priyanshu Mishra on Brilliant.org, but now has been deleted):
$$\sum _{n=2}^{25}
\frac{(n+1)!-n!}{n^{18}+n^{17}+n^{15}}$$
...
user485639
0
votes
0
answers
66
views
Limit in sum and fraction
I'm staring at
$$ f(n) = \sum_{x=1}^n a(n)^{n-x}\\
a(n) = \frac{(1 - \frac{f}{n})y}{y(1 - \frac{f}{n} - \frac{\delta}{n}) + \frac{\delta}{n}}$$
where $f$, $y$, $\delta$, all $ \in (0, 1)$, and $n$ ...
- 1,089
0
votes
1
answer
213
views
Is there a summation formula for this equation (contains square roots, and functions within the square root)?
I am trying to solve a summation formula that is quite complex. However, to make the "answering" process for you guys easier I'll isolate the part I am having trouble with...
The equation is as ...
