A Question on Summation

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The Student

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Does ∑5 from 0 to n = 3 equal 5 + 5 + 5 + 5. Is it also equivalent to ∑5 from 1 to n = 4?
 
The Student said:
Does ∑5 from 0 to n = 3 equal 5 + 5 + 5 + 5. Is it also equivalent to ∑5 from 1 to n = 4?
Click to expand...

Your post should be closer to:
"Does ∑5 from n = 0 to 3 equal 5 + 5 + 5 + 5?\(\displaystyle \ \ \) Is it also equivalent to ∑5 from n = 1 to 4?"


The variable for the counter is to go in front of (prior to) the counts, as in "n = 0" and "n = 1."


\(\displaystyle Else, \ \ what \ \ you \ \ wrote\ \ is \ \ equivalent \ \ to \ \ these: \ \ \displaystyle\sum_{ 0}^{n = 3} \ 5 \ \ \ \ \ and \ \ \ \ \ \displaystyle\sum_{1}^{n = 4} \ 5\)


But those are meaningless forms.
 
lookagain said:
Your post should be closer to:
"Does ∑5 from n = 0 to 3 equal 5 + 5 + 5 + 5?\(\displaystyle \ \ \) Is it also equivalent to ∑5 from n = 1 to 4?"


The variable for the counter is to go in front of (prior to) the counts, as in "n = 0" and "n = 1."


\(\displaystyle Else, \ \ what \ \ you \ \ wrote\ \ is \ \ equivalent \ \ to \ \ these: \ \ \displaystyle\sum_{ 0}^{n = 3} \ 5 \ \ \ \ \ and \ \ \ \ \ \displaystyle\sum_{1}^{n = 4} \ 5\)


But those are meaningless forms.
Click to expand...
Why are they meaningless? The first means 5 (n=0)+ 5 (n= 1)+ 5 (n= 2)+ 5 (n= 3)= 5+ 5+ 5+ 5= 20. The second means 5 (n=1)+ 5 (n= 2)+ 5 (n= 3)+ 5 (n= 4)= 5+ 5+ 5+ 5= 20.
 
HallsofIvy said:
Why are they meaningless? The first means 5 (n=0)+ 5 (n= 1)+ 5 (n= 2)+ 5 (n= 3)= 5+ 5+ 5+ 5= 20. The second means 5 (n=1)+ 5 (n= 2)+ 5 (n= 3)+ 5 (n= 4)= 5+ 5+ 5+ 5= 20.
Click to expand...

\(\displaystyle \ \displaystyle\sum_{ 0}^{n = 3} \ 5 \ \ne \ \displaystyle\sum_{n = 0}^3 \ 5\)


\(\displaystyle \displaystyle\sum_{1}^{n = 4} \ 5 \ \ne \ \displaystyle\sum_{n = 1}^4 \ 5 \)



Each form on the left-hand side (which was is the order expressed by the OP) of its respective "not equal to" sign
is meaningless. It's not in a proper summation form.


Some sources:


http://www.math.montana.edu/frankw/ccp/general/sigma/learn.htm


http://www.mathsisfun.com/algebra/sigma-notation.html

http://mathandmultimedia.com/2010/01/11/how-to-use-the-summation-symbol/


https://www.math.ucdavis.edu/~kouba/CalcTwoDIRECTORY/summationdirectory/

***** Edit: HallsofIvy, lets *not* be politically correct (read: misstate here). Not only was it not in "standard form," it wasn't in any correct form.*****
 
Last edited:
Okay, you are right. But while it was not in "standard" form (not too unusual for "Beginning Algebra" posts!) it was pretty clear what was meant.
 
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