For n an arbitrary positive integer, find a formula for 1 + 2 +
3 + · · · + n by summing the identity (m + 1)^{2} −
m^{2} = 2m + 1 from m = 1 to n.

Using your result from part (i) together with the identity (m +
1)^{3} − m^{3} = 3m^{2} + 3m + 1 , find a
formula for the sum 1^{2} + 2^{2} + 3^{2} +
· · · + n ^{2} .

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