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 ...
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 ...
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 ...
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 ‫‪ $\sum k = 1 +\... 1answer 3k views ### 'Plus' Operator analog of the factorial function? [duplicate] Possible Duplicate: What is the term for a factorial type operation, but with summation instead of products? Is there a similar function for the addition operator as there is the factorial ... 6answers 126 views ### Why does$ 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 ... 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: ... 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 ... 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: $$n>0,\quad n! = n \times (n-1) \times \cdots \... 2answers 75 views ### The integer sum jump series for x[x] [duplicate] I am trying to remember what the series 1+2+3+4+5+...+n is equal to in order to determine the series of breaks within the graph of x[x]. I know it obviously diverges as it goes to infinity, but what ... 7answers 11k views ### I have the pattern: 1 + 2 + 3 + 4 + 5 + 6, but I need the formula for it I'm writing some software that takes a group of users and compares each user with every other user in the group. I need to display the amount of comparisons needed for a countdown type feature. For ... 4answers 8k views ### How to find n'th term of the sequence 3, 7, 12, 18, 25, \ldots?$$3, 7, 12, 18, 25, \ldots$$This sequence appears in my son's math homework. The question is to find the n'th term. What is the formula and how do you derive it? 3answers 853 views ### When is a factorial of a number equal to its triangular number? Consider the set of all natural numbers n for which the following proposition is true.$$\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=\... 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 ...