Linked Questions

83
votes
30answers
173k views

Proof for formula for sum of sequence $1+2+3+\ldots+n$?

Apparently $1+2+3+4+\ldots+n = \dfrac{n\times(n+1)}2$. How? What's the proof? Or maybe it is self apparent just looking at the above? PS: This problem is know as "The sum of the first $n$ positive ...
51
votes
4answers
121k views

Factorial, but with addition [duplicate]

Is there a notation for addition form of factorial? $$5! = 5\times4\times3\times2\times1$$ That's pretty obvious. But I'm wondering what I'd need to use to describe $$5+4+3+2+1$$ like the ...
18
votes
4answers
3k 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 ...
4
votes
2answers
523 views

Finding a formula to sum natural numbers up to $n$ [duplicate]

Possible Duplicate: What is the term for a factorial type operation, but with summation instead of products? I got this question in homework: Find an expression for the sum ‫‪ $\sum k = 1 +\...
5
votes
1answer
3k views

'Plus' Operator analog of the factorial function? [duplicate]

Possible Duplicate: What is the term for a factorial type operation, but with summation instead of products? Is there a similar function for the addition operator as there is the factorial ...
1
vote
6answers
126 views

Why does $ 1+2+3+\cdots+p = {(1⁄2)}\cdots(p+1) $ [duplicate]

I saw this from Project Euler, problem #1: If we now also note that $ 1+2+3+\cdots+p = {(1/2)} \cdot p\cdot(p+1) $ What is the intuitive explanation for this? How would I go about deriving the ...
1
vote
1answer
77 views

Is there a way to quickly know the number of elements on a triangle type? [duplicate]

Possible Duplicate: What is the term for a factorial type operation, but with summation instead of products? I don't technically know the mathematical term, but imagine: ...
1
vote
0answers
139 views

What is this called? [duplicate]

Possible Duplicate: What is the term for a factorial type operation, but with summation instead of products? I am looking for the name of an operation similar to factorial. Factorial would be ...
1
vote
0answers
134 views

Is there a standard name or shorthand for “plustorial”? [duplicate]

Possible Duplicate: What is the term for a factorial type operation, but with summation instead of products? We're all familiar with factorial: $$n>0,\quad n! = n \times (n-1) \times \cdots \...
0
votes
2answers
75 views

The integer sum jump series for x[x] [duplicate]

I am trying to remember what the series 1+2+3+4+5+...+n is equal to in order to determine the series of breaks within the graph of x[x]. I know it obviously diverges as it goes to infinity, but what ...
4
votes
7answers
11k views

I have the pattern: 1 + 2 + 3 + 4 + 5 + 6, but I need the formula for it

I'm writing some software that takes a group of users and compares each user with every other user in the group. I need to display the amount of comparisons needed for a countdown type feature. For ...
2
votes
4answers
8k views

How to find $n$'th term of the sequence $3, 7, 12, 18, 25, \ldots$?

$$3, 7, 12, 18, 25, \ldots$$ This sequence appears in my son's math homework. The question is to find the $n$'th term. What is the formula and how do you derive it?
3
votes
3answers
853 views

When is a factorial of a number equal to its triangular number?

Consider the set of all natural numbers $n$ for which the following proposition is true. $$\sum_{k=1}^{n} k = \prod_{k=1}^{n} k$$ Here's an example: $$\sum_{k=1}^{3}k = 1+2+3 = 6 = 1\cdot 2\cdot 3=\...
3
votes
5answers
386 views

Can you explain this please $T(n) = (n-1)+(n-2)+…1= \frac{(n-1)n}{2}$ [duplicate]

Possible Duplicate: Proof for formula for sum of sequence 1+2+3+…+n? Can you explain this please $$T(n) = (n-1)+(n-2)+…1= \frac{(n-1)n}{2}$$ I am really bad at maths but need to ...
3
votes
2answers
420 views

Calculating a random “blob” in a 10 x 10 grid

The problem: You have a 10 x 10 grid where each cell can be either occupied (1) or unoccupied (0). All occupied cells in the grid are part of a single "blob": a single shape defined by a set of ...