Create sum expression from algebraic expression

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December 14th 2011, 07:23 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?
December 14th 2011, 07:52 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:

$x+\dots+11x=(1+\dots+11)x=\frac{11\cdot12}{2}x=66x$
December 14th 2011, 08:03 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
December 14th 2011, 08:07 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."
December 14th 2011, 08:34 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?
December 14th 2011, 08:40 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).
December 14th 2011, 04:53 PM
silver163

re: Create sum expression from algebraic expression

I haven't dealt with calculus in a while, thank you very much.
January 13th 2012, 01:27 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
January 13th 2012, 02:28 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 [tex]\sum_{i=1}^{12} ix[/tex] 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 $5\cdot 8x$ .
January 13th 2012, 07:29 PM
silver163

Re: Create sum expression from algebraic expression

The 500, 900 is labeling. but are the calculations correct?
January 14th 2012, 04:46 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.
January 14th 2012, 09:41 AM
silver163

Re: Create sum expression from algebraic expression

so would it be correct:

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

?
January 14th 2012, 09:48 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.
January 14th 2012, 12:15 PM
silver163

Re: Create sum expression from algebraic expression

ok is this statement true?

$\sum_{i=1}^6ix$ + $\sum_{i=1}^58x$ = 680000
January 14th 2012, 12:30 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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