MATH1081 Help (1 Viewer)

[Reikira]

Can someone please explain to me what happened from line 3 to line 4

http://i.imgur.com/mtWFt.png

 

[Timothy.Siu]

They just wanted to simplify the summations, so they made all of them go from 3 to n-2,
hence they expanded out whatever terms were left over, so for the first summation, they expanded out k=1 and k=2 which gives the 4 + 2 at the front.
the summations magically cancelled out which was lucky though.

 

[Reikira]

How did they transform the ( k = 2 to n - 2 ) to (k = 3 to N - 2) and (k = 3 to N) to ( k = 3 to N -2 )

 

[unsw-maths-guru]

This is just like writing
sum(k^2,k=1..N-1) = 1 + 2^2 + ... + (N-2)^2 + (N-1)^2
= 1 +4+ (N-1)^2 + sum(k^2,k=3..N-2)
As TS said, when you put all the sums to be over the same k's so you can combine them, you get several terms left over.

 

[Reikira]

OH! i kind of get it now. One more question. Why was (k = 3 ... N - 2) selected instead of other values like (k = 4 ... N - 3) or something?

 

[Timothy.Siu]

OH! i kind of get it now. One more question. Why was (k = 3 ... N - 2) selected instead of other values like (k = 4 ... N - 3) or something?

because it was the biggest range that all of the summations had.
you could choose k=4...N-3, but then you'd be wasting some time expanding out parts that you didn't need to.