How to Simplify a Summation with Unknown Last Term?

[mohabitar]

I'm having a hard time understanding what this question is even asking for. Do I just write this summation in closed form? What does it mean by its last term, or the k=n term? I know I'm supposed to have at least attempted the problem, but I honestly have no idea what this question is even asking from me to begin with.

 

[Mark44]

This is a finite sum with (n - 3) + 1 terms. All they're asking for is a summation consisting of the first n - 3 terms + the last term; i.e., the term when k = n.

To get the first summation, the index k should run from k = 3 to k = ?

 

[mohabitar]

to k=n-1? And the 2nd summation would just be for the actual value of n, correct? But there are two parts to this right? First break it up into its two parts, then write a summation that contains everything but its last term, so that would be everything from k=n-1.

 

[mohabitar]

Here's what I got so far:
Am I done? What else are they asking for?

 

[Mark44]

to k=n-1? And the 2nd summation would just be for the actual value of n, correct? But there are two parts to this right? First break it up into its two parts, then write a summation that contains everything but its last term, so that would be everything from k=n-1.

Everything from k = 3 to k = n - 1. There isn't really a second summation - you could write it as a summation, but it consists of just a single term, so writing it in summation form is overkill.

 

[Mark44]

In your reply with the scan, you aren't getting it. The last term part should not be written as a summation. It is a single term.

The "remaining terms" part is wrong. Your summation represents only the last two terms of the original summation. It should include the first term, second term, ..., (n - 1)st term.