0
votes
0answers
35 views

Precise notation of a sum of a sequence

I need help in rewriting the support of a function $f$ in a more compact or precise way given its upper bound $b$ and lower bound $a$ as \begin{eqnarray} b&=&\max\left( \sum_{n}\alpha_n ...
16
votes
4answers
2k views

Is there a way to denote the calculation $1+2+3+\dots+n$? [duplicate]

Since $n!$ represents $$1\cdot2\cdot3\cdots n,$$ I am wondering if there is a way to represent $$1+2+3+\dots+n?$$ What are some usual notations for the computation of some common sequences? Any other ...
1
vote
2answers
26 views

Difference between $\lim_{n\rightarrow\infty}\sum_{k=1}^{n}a_k$ and $\sum_{k=1}^{\infty}a_k$

Is there any difference between $\lim_{n\rightarrow\infty}\sum_{k=1}^{n}a_k$ and $\sum_{k=1}^{\infty}a_k$? My example and thought: Let $a_n=n$ where $n\in\mathbb{P}$. $\mathbb{P}$ is the set of all ...
0
votes
1answer
34 views

Summation notation rule

Sorry if this sounds elementary, but I have problems with the following in a text I am reading: $$ \left(\sum_{k=0}^{n} C_k\phi_k(x)\right)^2 = \sum_{k=0}^{n}\sum_{l=0}^{n}C_k ...
1
vote
1answer
25 views

Summation notation for time series

I need to add together the results of a function for four consecutive years prior to the start of a project. The function is calculated for individual years. It is (10 × (A + B + C) ÷ ...
1
vote
1answer
65 views

Simplification of a nested sum

I have a nested sum like so: $$\underbrace{\sum_{k_1=k_0}^{k^*} \ ... \sum_{k_n=k_{n-1}}^{k^*}}_{\text{n times}} 1\quad\ \text{with}\ \ n, k_0, k^* \in \mathbb{N},\ k^*\geq k_0$$ Is there a general, ...
0
votes
1answer
30 views

Notation for nested sigmas (summations)

Is there any standard notation, other than an ellipsis, for a chain of nested sigma summations? For instance, I have: $$ \sum_{b_0=0}^{L} \sum_{b_1=0}^{L-b_0} \sum_{b_2=0}^{L-b_0-b_1} \cdots ...
0
votes
1answer
28 views

Doing an operation to every number in a subscript

I'm not good with words, and neither with math, but I'll do my best. (If someone has a better title for this then...). I've been learning about subscripts recently, and things like $\sum$ and $\prod$. ...
2
votes
2answers
49 views

Multiplying subscripts

I'm not too good with math, but once in a while I like to fiddle around with it. But one question has been bugging me lately. Let's say I have $x_{1} = 1$, $x_{2} = 2$, etc, $x_{352} = 352$. Is there ...
0
votes
0answers
25 views

A question regarding notation of equation

I'm reading a research paper, and, have come across this summation equation $$ S_{2} = \sum_{N -1}^{j = 0}w_{j}^{2}\cdot $$ My question is: if j = 0..... N-1 do I ...
1
vote
2answers
92 views

Notation for summing all elements under the diagonal of a square matrix

I have a simple question: What is the notation for summing all elements under the diagonal of a square matrix? I appreciate your help.
2
votes
3answers
41 views

Summation of elements of a Set [Notation]

Is there any compact Notation to express the summation of all the elements of a set?
-2
votes
2answers
84 views

How to use math symbols to represent a basic formula

I've a fomula that looks like this: How to properly represent this formula using SUM Symbol and MEAN symbol? $$ r=2 \left(3(f_1) +\frac{(g_1+...+ g_n)}{n} + \frac{s_1 +... + s_n}{n}\right) + x_1 ...
1
vote
3answers
53 views

Is it possible to change the step interval on a sum?

Suppose we wanted to create a sum that says, from n=0 to n=16, n will add 4 to itself and add the function like a regular sigma form. Quite similar to: ...
1
vote
1answer
60 views

Combining set builder and summation notation

What's the best notation for the sum of a subset? Given $S = \{1,2,3,4,5,6,7\}$, let's say I want to find the sum of the squares of elements less than 4. Initially I used the following notation: ...
0
votes
2answers
29 views

How to repesent n x m multiplication into symbol notation?

I am not a mathematician and so I might not be using the right terms. I have a vector of n components and another vector of m components ...
1
vote
1answer
23 views

summation index notation, specify all variables?

I am reading lecture slides for a logistics course and for one of the Linear Programming contrainsts, the summation is written as follows: $$ \sum_{i \in I} X_{ij} $$ and $$ \sum_{c \in C} Y_{jc} ...
0
votes
0answers
17 views

Skip specifying sets under summation signs

I have a couple of summations that all have the notation below them that s is an element of S, k is an element of K, etc. The set S or K is not given but assumed to be generally known. $$ \sum_{k ...
2
votes
1answer
29 views

Repeated Summation function

I am writing a solution to a question, and the solution requires a lot of $\sum$ functions, is there a way to notate many $\sum$ functions in a row? for example is there one function that can ...
1
vote
1answer
73 views

What is the definition of $\sum\limits_{0\leq i\leq m,\text{ }0\leq j\leq n}a_{ij}$

I understand the concept of double summations, at least intuitively, but I'm trying to understand it formally. So, to begin with, I have a question: Is this double summation equality true by ...
4
votes
2answers
75 views

Sum Notation with restrictions

I understand normal sigma notation but what does it mean when we place under a sum the restriction that $i + j + k = n$, for example? Is this simply $3$ sums in disguise or is it something else?
0
votes
0answers
128 views

Order of operations: summation and exponenets

I'm reading a paper that includes the following expression: $$\sum^c_{k=1}\left(\frac{||x_i - c_j||}{||x_i - c_k||}\right)^\frac{2}{m-1}$$ Should I read that the exponentiation to apply to the whole ...
1
vote
2answers
102 views

How to understand sum symbol?

I have searched google for an answer but I'm not sure what I'm asking. I know that Sigma means sum but there is an 'n' above Sigma and an 'i=1' under sigma. how can i understand this? thank you!
0
votes
2answers
129 views

I don't understand this notation… - Series with ln

I found this notation in my book $$ \sum\limits_{i=1}^n \ln^n3 $$ and I don't know how to interpret it. Is it $$ \sum\limits_{i=1}^n \ln((1^n)\cdot3)\;? $$ And btw, how to check if this series ...
1
vote
1answer
97 views

Notation for Multiple summation

Is there an alternate way to represent the multiple summation given below? $\sum_{i_k=k}^{n} \sum_{i_{k-1}=k-1}^{i_k} \dots \sum_{i_2=2}^{i_3} \sum_{i_1=1}^{i_2}$ It guess it is wrong to write it as a ...
0
votes
1answer
70 views

correct expansion of a sum using multiple indexes

I have looked for a similar posting but haven't found anything... but then I am also a bit unsure of how to search because I've never posted a math question before. In my introductory finite element ...
4
votes
4answers
97 views

Big Greeks and commutation

Does a sum or product symbol, $\Sigma$ or $\Pi$, imply an ordering? Clearly if $\mathbf{x}_i$ is a matrix then: $$\prod_{i=0}^{n} \mathbf{x}_i$$ depends on the order of the multiplication. But, ...
3
votes
2answers
90 views

Summation and Product Bounds

If I have a sum or product whose upper index is less than its start index, how is this interpreted? For example: $$\sum_{k=2}^0a_k,\qquad \prod_{k=3}^1b_k$$ I want to say that they are equal to the ...
2
votes
2answers
138 views

Einstein Summation with multiple terms

I know the basics of Einstein Summation but i've got an equation here that is a little more complex than the easy examples i'm only finding on this subject: $C = (p-nT) \partial_\gamma u_\gamma + ...
3
votes
1answer
84 views

Notation: What is the scope of a sum?

I would interpret $\sum_{i=1}^2 x_i + y$ as $x_1 + x_2 + y$, but I would interpret $\sum_{i=1}^2 x_i + y_i$ as $x_1 + y_1 + x_2 + y_2$. I realize this is a little inconsistent. Should the latter be ...
4
votes
2answers
181 views

Summation/Sigma notation

There are lots of variants in the notation for summation. For example, $$\sum_{k=1}^{n} f(k), \qquad \sum_{p \text{ prime}} \frac{1}{p}, \qquad \sum_{\sigma \in S_n} (\operatorname{sgn} \sigma) a_{1 , ...
3
votes
1answer
68 views

Does this summation index make any sense?

From my textbook, I have this summation: $$ y_f(k) = \sum_{\tau = k_0}^{k-1}a^{k-1-\tau}g(\tau) $$ So far so good. But then there is a "change of variable" $\tau = \theta - m$ and the summation ...
1
vote
1answer
95 views

How to find a summation of a sequence?

I am working in analyzing an algorithm in recurrence, but I end up in the following sequence: $$\frac5{2^6}n^2+\frac5{2^4}n^2+\frac5{2^2}n^2+n^2$$ I tried to make an equivalent summation but I ...
3
votes
1answer
136 views

What does this notation (unmatched right parenthesis after a summation) mean?

My textbook contains this notation: $$\sum_{n=0}^{\infty} r^{2n}\cos n\theta \bigg) ^2 + \quad \sum_{n=0}^{\infty} r^{2n} \sin n\theta \bigg) ^2$$ What does this notation mean? Square the result of ...
3
votes
1answer
152 views

When using sigma notation, why is “1” put as value?

First of all, I never really learned exactly what Sigma notation is, and although I understand the basics, there are some things that are confusing me. I'm trying to convert the following algorithm to ...
1
vote
1answer
64 views

Sigma with Or Underneath

This is the notation found in Spivak's Calculus: Chapter 23: Infinite Series Theorem 9 What does $\displaystyle \sum_{i \text{ or }j > L} |a_i||b_j| $ mean?
0
votes
1answer
68 views

Why is the upper bound of this statement always incremented by 1?

Why is "for j = 1 to n" translate to this? Why is the upper bound always incremented by 1? $$\sum_{j=1}^{n+1}1 $$ Why isn't it $$\sum_{j=1}^n1 $$ "for j = 1 to n" is written in pseudo code btw ...
4
votes
1answer
146 views

Operators - sums, products, exponents, etc.

$(x + x + \cdots + x)$, where $x$ added $n$ times can be written as $x * n$. $(x * x * \cdots * x)$, where $x$ multiplied $n$ times can be written as $x ^ n$. Is there an operator, such that if ...
3
votes
1answer
77 views

Summation over a Vector

I am trying to find the Fourier series of a 3D function, $e^{-\alpha(x^2 + y^2 + z^2)}$ with bounds $-\ell_1 < x < \ell_1$, $-\ell_2 < y < \ell_2$, $-\ell_3 < z < \ell_3$. I have ...