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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 ...
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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 ...
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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 ...