Reikira
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Can someone please explain to me what happened from line 3 to line 4
http://i.imgur.com/mtWFt.png
http://i.imgur.com/mtWFt.png
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MATH1081 Help (1 Viewer)
- Thread starter Reikira
- Start date
Timothy.Siu
Prophet 9
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.
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.
unsw-maths-guru
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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.
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.
Timothy.Siu
Prophet 9
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.