Summation Notation for [(i^3)/(N^3)]

[Lo.Lee.Ta.]

I think I get summation notation when when there are more numbers than variables
6
Ʃ i/6 <---I can figure that out.
i=1

But I'm confused on how to find what this equals:
N
Ʃ (i^3)/(N^3) = ?
i=1

How do you add something N times? ...I could deal with a number like 6, but I'm confused about N...

Any help? :/

Thank you! :)

 

[Mark44]

I think I get summation notation when when there are more numbers than variables
6
Ʃ i/6 <---I can figure that out.
i=1

But I'm confused on how to find what this equals:
N
Ʃ (i^3)/(N^3) = ?
i=1

How do you add something N times? ...I could deal with a number like 6, but I'm confused about N...

Any help? :/

Thank you! :)

The first term in the summation is 1/N³.
The second term is 8/N³.

Can you continue?
What is the last term in the summation?

You will necessarily need to use an ellipsis (i.e., "..." ) when you expand this summation.

 

[Lo.Lee.Ta.]

So the (N)^3 in denominator is just kept as (N)^3!

Okay, would this be the answer then:

1/(N^3) + 8/(N^3) + 27/(N^3) + ... + ((N-1)^3)/(N^3) + (N^3)/(N^3)

 

[Dick]

So the (N)^3 in denominator is just kept as (N)^3!

Okay, would this be the answer then:

1/(N^3) + 8/(N^3) + 27/(N^3) + ... + ((N-1)^3)/(N^3) + (N^3)/(N^3)

Yes, if that's the form you want the answer in. If you actually want to sum it up there is a formula for 1^3+2^3+3^3+...+N^3. Just like there is a formula for 1+2+3+...+N=(N+1)N/2. Probably easiest to try and look it up unless you are required to prove it.