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What is the mathematical term for this? It's something like a factorial.

I honestly don't even know how to phrase this question, so let me demonstrate it with an example:

If the count is 1 then the formula is x = 1y
If the count is 2 then the formula is x = 1y + 2y
If the count is 3 then the formula is x = 1y + 2y + 3y
If the count is 4 then the formula is x = 1y + 2y + 3y + 4y

etc..

What is this called? And bonus question: is there a way to do this in Excel?

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    Coudld you clarify what the "count" is? And could you clarify what the variables $x,y$ indicate? – 2017-02-15
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    I think this question can be interpreted as the recursive definition of $x$ based on the expression of $x$ at a lower count (number of terms) and not about [factorial](https://en.wikipedia.org/wiki/Factorial). This question is asking, "in mathematics, the \_\_\_\_ of a non-negative integer n, is the sum of all positive integers less than or equal to n." – 2017-02-15
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    @S.C.B. the "count" is the number of terms in the final formula. X and Y don't represent anything in particular, they are just there to illustrate the concept. In my specific usage, Y represents a combination of velocity and time and x represents the total distance. – 2017-02-15
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    Just for funs, your x=1y, x=1y+2y, etc. looks like a triangle :-) – 2017-02-15

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Factor out all the $y$'s and you get

$$x_n=y(1+2+3+\dots+n)=yT_n$$

where $T_n$ is a triangle number. We know that $T_n=\frac{n(n+1)}2$, thus,

$$x_n=\frac{yn(n+1)}2$$

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    Is there a name for this process? – 2017-02-15
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    Follow the link on triangle numbers and you will find all the answers! – 2017-02-15
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    What if your range isn't 1 through n but rather (n-5) through n? – 2017-02-15
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    You take one triangle number and subtract a smaller triangle number. What do you get? – 2017-02-15