All Questions
18
questions
1
vote
0
answers
47
views
Is there a rule for using parentheses or brackets after the summation symbol to indicate what is included in the sum? [duplicate]
Using parentheses or brackets removes ambiguity but is it necessary?
- 19
0
votes
2
answers
124
views
Pi/product notation property applications problem
I have recently attempted to simplify this
$$ P(n) = \prod_{v=2}^{n} (2 + \frac{2}{v^2 - 1}) $$
I have reached an answer (which is wrong) through the following steps:
rearranging what is inside the ...
- 15
3
votes
6
answers
79
views
Why do $\sum_{i=0}^3 (-2^i)$ and $\sum_{i=0}^3 ((-2)^i)$ give different values?
On my TI-84, I have noticed something weird.
I have:
$$\sum_{i=0}^3 (-2^i) = -15$$
and
$$\sum_{i=0}^3 ((-2)^i) = -5$$
Does anybody know why these sum to a different number?
Correct me if I am wrong ...
- 51
2
votes
1
answer
64
views
The significance of two symbols
Excuse me for this canonical or simple question. But someone, please, can explain me, also with simplest example for a teacher of an high school, the significance of these symbols/operators?
$$\sum_{\...
- 7,814
6
votes
3
answers
190
views
How to read and execute $\sum_{1 \leq \ell <m<n} \frac{1}{5^{\ell}3^{m}2^{n}}$
How to read and execute this sum?
$$\sum_{1 \leq \ell <m<n} \frac{1}{5^{\ell}3^{m}2^{n}}$$
I am having trouble to understand where is my error.
The question does not say, but I am assuming that ...
-1
votes
3
answers
51
views
Summation notation for $1*3+2*4+3*5+...+40*42$
For this pattern $1*3+2*4+3*5+...+40*42$
my summation notation was: $\sum_{i=1}^n i(i+2), n = 40$
Which gives me the answer of $23780.$
Is this correct notation?
- 1
3
votes
1
answer
149
views
Finite unordered sums
For all $n \geqslant 1,$ let $I_n = \{1, 2, \ldots, n\}.$
Let $X$ be a commutative semigroup.
Let $(x_i)_{i \in I_n}$ be a finite sequence in $X.$ That is to say,
let $x \colon I_n \to X$ be any ...
- 12.3k
0
votes
0
answers
67
views
Naming a sum such as $\sum\limits_{x=1}^{n}{x}=\frac{n(n+1)}{2}$
If we let consider a simple sum such as the following:
$$\sum_{x=1}^{n}{x}=\frac{n(n+1)}{2}$$
Would it be correct to name the function that equals $\sum\limits_{x=1}^{n}{x}$ for a given upper bound,...
- 1,619
-1
votes
2
answers
112
views
What is the difference between the summations?
What is the difference between the summation $$\sum_{1 \leq i<j \leq n} f(i,j)$$ and $$\sum_{1\leq i} \sum_{<j \leq n} f(i,j)?$$
4
votes
4
answers
650
views
Notation of symmetric sum notation
When you use the symmetric sum notation, for example, $$\sum_\text{sym}abc+a$$ if there are 3 variables, then does abc count once, 3 times or 6 times?
I am confused about repetitions of the same ...
- 4,934
0
votes
2
answers
130
views
Sigma notation for repetitions of 1.01(n+200)
This sounds odd but, there was a math question in my textbook which intrigued me. So it goes ‘Sarah puts $200 in her account every month, which is subject to 1% interest. Show the value of money in ...
0
votes
1
answer
25
views
How to reorder a vector with calculus from max to min for an order-specific summation using calculus?
I have a vector $V$ containing a set of finite numbers ranging between $0.0$ and $1.0.$
However, they may not be in consecutive order. How can I reorder them with a calculus formula? Even better, ...
- 103
4
votes
2
answers
117
views
Which one is correct $\sum_{n=1}^{k} 2^{n}× n^2$ or $\sum_{n=1}^{k} (2^{n}× n^2)$?
I have $2$ questions about notation.
Question 1.
Suppose, numbers are as follows.
$\left\{3\right\}\longrightarrow7$
$\left\{3,6\right\}\longrightarrow9$
$\left\{3,6,7\right\}\longrightarrow11$
$\...
- 477
0
votes
0
answers
201
views
Redefining a Variable in terms of itself vs creating a new one
Suppose I want to show
$$\sum_{n=1}^{\infty}ar^{n-1} = \sum_{n=0}^{\infty}ar^{n}$$
Is it acceptable to increment $n$ by redefining it in terms of itself, i.e., $n = n+1$ (written n+=1 in many ...
- 1,196
2
votes
1
answer
111
views
Need help with inductive proof of Binomial Theorem
I'm new to math and trying to learn about the Binomial Theorem, by following this tutorial.
I got stuck trying to read the Induction Proof.
They give an example of using the Sum notation:
$$ (x + y)^...
- 23