Summation question

[joshmccraney]

hey pf!

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

thanks!

josh

 

[Mark44]

hey pf!

can someone explain to me what to do if presented with an equation like this: $$\sum_{i=1}^{n}A_i=i$$
is this identical to stating $A_i=i$? 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]

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]

yea, i was trying to generalize for determining the Fourier coefficients. i have a link here on pf: https://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.