ReIndexing a Series(non-infinite)

[jack612blue]

Homework Statement

Homework Equations

The Attempt at a Solution

#7 only
I'm stumped, i have no idea as to what to do.

I can't even find help on the internet/book. Its almost like this topic doesn't even exist.

I know both upper and lower limits have been decreased by 2

 

[Dick]

Homework Statement

Homework Equations

The Attempt at a Solution

#7 only
I'm stumped, i have no idea as to what to do.

I can't even find help on the internet/book. Its almost like this topic doesn't even exist.

I know both upper and lower limits have been decreased by 2

Ok, then also change k to k+2. Doesn't that make sense? It would offset the other change.

 

[jack612blue]

Ok, then also change k to k+2. Doesn't that make sense? It would offset the other change.

Hello,

Thank you for responding.

I understand that part

6
sigma
1

I'm just confused as to what to put in the inside.

I found this on wikipedia. is this relevant?

 

[Sourabh N]

Define a new variable, say, j. How should j and k be related so that j goes from 1 to 6 when k goes from 3 to 8?

 

[SammyS]

I found this on Wikipedia. Is this relevant?

Yes, it's relevant .

 

[HallsofIvy]

It's really just an algebraic substitution. The series, as given, starts with k= 3 and we want to change that to a series starting at 1. Rather than use "k" to mean two different things, I am going to call this second index "i". That is, we want i= 1 to correspond to k= 3. That is the same as saying k- i= 3- 1= 2 so that k= i+ 2 or i= k- 2.

When k= 8, i= 8- 2= 6 so the series goes from i= 1 to 6 as desired. And in the formula for the terms of the series, since, as above, k=i+ 2, replace each k with i+ 2. d What do you get when you replace "k" in "2k- 1" with "i+2"?

You will get a series in i. Since the "index" is a dummy, and has no meaning in the total sum, you can, to completely match what is required, simply replace "i" with "k" again.