Create sum expression from algebraic expression

emakarov

but are the calculations correct?
No.

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.

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 $\displaystyle \sum_{i=7}^5ix$, where the upper limit is less than the lower one.

silver163

so would it be correct:

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

?

emakarov

This is not an equation (it does not have an = sign), so I can't say if it's true or false.

silver163

ok is this statement true?

$\displaystyle \sum_{i=1}^6ix$+$\displaystyle \sum_{i=1}^58x$ = 680000

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emakarov

$\displaystyle \sum_{i=1}^6ix+\sum_{i=1}^58x=\left(\sum_{i=1}^6i+\sum_{i=1}^58\right)x=(21+40)x=61x$. However, in [post=707449]post #8[/post] the expression labeled 500 has $\displaystyle 1x+2x+3x+4x+5x+6x+7x+8x+8x+8x+8x+8x$ = $\displaystyle \sum_{i=1}^7ix+\sum_{i=1}^58x = 28x+40x = 68x$, which is indeed 680000 for x = 10000.

silver163

Oh ok I see my mistake now, I was confused on the use of the subscripts. Now I understand how to write them correctly. Thank you very much, I really appreciate it.

silver163

how come I cannot set the upper script 12?

$\displaystyle \sum_{i=1}^{12}80000x=960,000$

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emakarov

You need to wrap the upper limit {12} in curly braces in LaTeX.

Again, this is not an equation, so I can't say if it true or false. This thread is becoming big, and I am having trouble getting your implied references to earlier posts.

silver163 = 780000 = 680000 = 570000

Are any of those statements true?

emakarov

The first two are true for x = 10000. The third becomes true if you replace 8x by 6x, as in post #8.