# Create sum expression from algebraic expression

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• Dec 14th 2011, 08:23 AM
silver163
Create sum expression from algebraic expression
Hello,

I am trying to create a summation equation from this algebra equation, would it be possible?

x+2x+3x+4x+5x+6x+7x+8x+9x+10x+11x

If so can anyone help me?
• Dec 14th 2011, 08:52 AM
emakarov
re: Create sum expression from algebraic expression
Strictly speaking, this is not an equation because it lacks the = sign. It's an expression. If by "summation equation" you mean an expression that uses the $\sum$ symbol, then

$x+2x+3x+4x+5x+6x+7x+8x+9x+10x+11x=\sum_{i=1}^{11}( ix)$

If you want to simplify that expression, then you can use the formula for the sum of an arithmetic progression:

$x+\dots+11x=(1+\dots+11)x=\frac{11\cdot12}{2}x=66x$
• Dec 14th 2011, 09:03 AM
silver163
re: Create sum expression from algebraic expression
Thank you for the response, I understand that in order to create the equation that symbol is needed but my question is would it be possible to convert the equation I posted into that summation? if so how?

basically it works by set periods for example if the period is set to 3 then the equation would be: x+2x+3x and if the period is set to 4 then the equation would be x+2x+3x+4x
• Dec 14th 2011, 09:07 AM
emakarov
re: Create sum expression from algebraic expression
$x+2x+\dots+nx=\frac{n(n+1)}{2}x$

Edit: If this is not what you want, please explain what you mean by "that summation."
• Dec 14th 2011, 09:34 AM
silver163
re: Create sum expression from algebraic expression
Hello,

Yes I needed a formula and that one is good. I guess I was thinking that the formula could have been written using the summation symbol?
• Dec 14th 2011, 09:40 AM
emakarov
re: Create sum expression from algebraic expression
The formula with the summation symbol is given in post #2 (you can replace 11 with $n$ and add ... in the left-hand side).
• Dec 14th 2011, 05:53 PM
silver163
re: Create sum expression from algebraic expression
I haven't dealt with calculus in a while, thank you very much.
• Jan 13th 2012, 02:27 PM
silver163
Re: Create sum expression from algebraic expression
Hello,

I wanted to ask if I got these written correctly:

900: 1x+2x+3x+4x+5x+6x+6x+6x+6x+6x+6x+6x
500: 1x+2x+3x+4x+5x+6x+7x+8x+8x+8x+8x+8x
100: 1x+2x+3x+4x+5x+6x+7x+8x+9x+10x+11x+12x

For these would the equation be correct written:

900: S (upper: 5 lower: 1) ix + S (upper:6 lower: 1) 6x where x = 10000
500: S (upper: 5 lower: 7) ix + S (upper:5 lower: 1) 6x where x = 10000
500: S (upper: 12 lower: 1) ix where x = 10000
• Jan 13th 2012, 03:28 PM
emakarov
Re: Create sum expression from algebraic expression
I don't see the relationship between 900, 500, 100 and the expressions after the colon.

In this forum, you can write $$\sum_{i=1}^{12} ix$$ to get $\sum_{i=1}^{12} ix$.

Below $\sum$ (capital Greek sigma) we typically write $i = 1$, not just 1, but above $\sum$ we write just 12 (for example). The notation $\sum_{i=1}^{12}$ means the sum where $i$ ranges from 1 to 12.

Quote:

500: S (upper: 12 lower: 1) ix where x = 10000
$\sum_{i=1}^{12}ix$ is indeed 1x+2x+3x+4x+5x+6x+7x+8x+9x+10x+11x+12x regardless of the value of x.

Quote:

500: S (upper: 5 lower: 7) ix + S (upper:5 lower: 1) 6x where x = 10000
$1x+2x+3x+4x+5x+6x+7x=\sum_{i=1}^7ix$. To represent 8x+8x+8x+8x+8x you can write $\sum_{i=8}^{12}8x$, or $\sum_{i=1}^{5}8x$ (note that there is no $i$ after $\sum$, which means that all terms in the sum are the same), or just $5\cdot 8x$.
• Jan 13th 2012, 08:29 PM
silver163
Re: Create sum expression from algebraic expression
The 500, 900 is labeling. but are the calculations correct?
• Jan 14th 2012, 05:46 AM
emakarov
Re: Create sum expression from algebraic expression
Quote:

Originally Posted by silver163
but are the calculations correct?

No.

Quote:

Originally Posted by silver163
900: 1x+2x+3x+4x+5x+6x+6x+6x+6x+6x+6x+6x
...
900: S (upper: 5 lower: 1) ix + S (upper:6 lower: 1) 6x where x = 10000

In the explicit sum, 6x occurs 7 times, but in the sigma-expression, it is used only 6 times.

Quote:

Originally Posted by silver163
500: 1x+2x+3x+4x+5x+6x+7x+8x+8x+8x+8x+8x
...
500: S (upper: 5 lower: 7) ix + S (upper:5 lower: 1) 6x where x = 10000

It is not clear what 6x is doing in the sigma-expression and why you have $\sum_{i=7}^5ix$, where the upper limit is less than the lower one.
• Jan 14th 2012, 10:41 AM
silver163
Re: Create sum expression from algebraic expression
so would it be correct:

$\sum_{i=1}^6ix$

?
• Jan 14th 2012, 10:48 AM
emakarov
Re: Create sum expression from algebraic expression
This is not an equation (it does not have an = sign), so I can't say if it's true or false.
• Jan 14th 2012, 01:15 PM
silver163
Re: Create sum expression from algebraic expression
ok is this statement true?

$\sum_{i=1}^6ix$+ $\sum_{i=1}^58x$ = 680000
• Jan 14th 2012, 01:30 PM
emakarov
Re: Create sum expression from algebraic expression
$\sum_{i=1}^6ix+\sum_{i=1}^58x=\left(\sum_{i=1}^6i+ \sum_{i=1}^58\right)x=(21+40)x=61x$. However, in post #8 the expression labeled 500 has $1x+2x+3x+4x+5x+6x+7x+8x+8x+8x+8x+8x$ = $\sum_{i=1}^7ix+\sum_{i=1}^58x = 28x+40x = 68x$, which is indeed 680000 for x = 10000.
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