Summation by differences

This is a method of finding the answer to problems involving summation. Let me know how to improve on this. I hope that I have not made any mistakes. I hope to upload some more. I am a supply teacher.

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Summation by difference
Find the sum of
n = 1 4 22 02
n = 2 8 32 12
n = 3 12 42 22 22 cancels out 22
n = 4 16 52 32 32 cancels out 32
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n =(n2) 4(n2) (n1)2 (n3) Note here that (n2+1) = (n1)
n =(n1) 4(n1) (n)2 (n2)2
n = n 4n (n+1)2 (n1)2 "n" is the last term
(n) + (n+1)2 02 12 is the answer ie. What's left
2
are the top two on the right and the bottom two on the left after
cancelling out. The blue lines show what have been cancelled out

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