Question

a little bit confused about summation rules

Answer 1

Try reading this: http://psychassessment.com.au/PDF/Chapter%2001.pdf

Answer 2

ok so I have this formula \[v_{av}=\frac{\sum^n_{i=1}v_i\delta t_i}{\sum^n_{i=1}\delta t_i}\]

Answer 3

yeah I have looked it up. I would just like some clarification on a problem I am working on

Answer 4

I also have that \[\delta t_i=\frac{2z_i}{v_i}\]

Answer 5

so plugging this in I get \[v_{av}=\frac{\sum^n_{i=1}v_i\frac{2z_i}{v_i}}{\sum^n_{i=1}\frac{2z_i}{v_i}}\]factoring out constants\[v_{av}=\frac{\sum^n_{i=1}v_i\frac{z_i}{v_i}}{\sum^n_{i=1}\frac{z_i}{v_i}}\]canceling\[v_{av}=\frac{\sum^n_{i=1}z_i}{\sum^n_{i=1}\frac{z_i}{v_i}}\]

Answer 6

now I am wondering if I can simplify this any further?

Answer 7

@TuringTest

Answer 8

\(v_i\) and \(z_i\) are all different terms depending on index, so I can't see how you could simplify that. I could be wrong...

Answer 9

right that's what my thinking was.

Answer 10

I mean, what about this?\[v_{av}=\frac{\sum^n_{i=1}\cancel v_i\frac{z_i}{\cancel v_i}}{\sum^n_{i=1}\frac{z_i}{v_i}}\]or am I misreading your notation?

Answer 11

\[\sum_i(v_i)\cdot(\frac{z_i}{v_i})=\sum_iz_i\]is valid

Answer 12

as long as it's under the same summation sign

Answer 13

hmm no I don't think that is correct. This is a physics problem and the answer does not make sense. v is a velocity and z is a distance so the final sum is a velocity.

Answer 14

or final answer I should say.

Answer 15

you are right, that rule wouldn't make sense mathematically either

Answer 16

actually the more I thinking about it the more I am thinking it should make sense, but I am obviously unsure...
@Zarkon @satellite73 series rules question

Answer 17

this is valid...

\[\sum_i\left[(v_i)\cdot\left(\frac{z_i}{v_i}\right)\right]=\sum_iz_i\]

Answer 18

right and I did that in the numerator of the fraction to get.
\[v_{av}=\frac{\sum^n_{i=1}z_i}{\sum^n_{i=1}\frac{z_i}{v_i}}\] Is there any way to express this as a product of \(z_i\) and \(v_i\) in the numerator?

Answer 19

unless you have more info...you can't simplify it any more

Answer 20

thanks