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Summation question

by joshmccraney
Tags: summation
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joshmccraney
#1
Jan20-14, 06:37 PM
P: 346
hey pf!

can someone explain to me what to do if presented with an equation like this: [tex]\sum_{i=1}^{n}A_i=i[/tex]
is this identical to stating [itex]A_i=i[/itex]? either way, can you please explain.

thanks!

josh
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Mark44
#2
Jan20-14, 06:44 PM
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P: 21,397
Quote Quote by joshmccraney View Post
hey pf!

can someone explain to me what to do if presented with an equation like this: [tex]\sum_{i=1}^{n}A_i=i[/tex]
is this identical to stating [itex]A_i=i[/itex]? either way, can you please explain.

thanks!

josh
It doesn't make much sense to me. On the left side, i is an index variable that takes on the values 1, 2, 3, ..., n, so I have no idea what it means on the right side.

Where did you see this? If it's from a textbook, can you post a picture?
AlephZero
#3
Jan20-14, 08:23 PM
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P: 7,280
Just taking it at face value, it means
##A_1 + A_2 + \cdots + A_n = i##

The ##i## in the sum is a "bound variable" or "dummy variable". You could replace it by anything else (except ##n##) without changing the meaning. The ##i## on the right hand side means ##i##.

But using ##i## twice in one equation like that is horrible, as Mark44 said. It would have been more literate to write something like
$$\sum_{k=1}^n A_k = i$$

joshmccraney
#4
Jan20-14, 08:29 PM
P: 346
Summation question

yea, i was trying to generalize for determining the fourier coefficients. i have a link here on pf: http://www.physicsforums.com/showthread.php?t=733877
my question there has been answered, but if you're curious to this type of problem, there's the link.


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