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We find a formula for the sum of the first n squares:Sn = 12 + 22 + 32 + 42+…+n2.We haveS1 = 1, S2 = 12 + 22 = 5, S3 = l2 + 22 + 32 = 14,S4 = 30, S5 = 55, S6 = 91.and so on. To make things a little simpler, we will also use the sum of the squares of the first zero terms , S0 = 02 = 0. Arranging these values in a table,we find thatSince the third differenes △3Sn are constant,these data values must follow a cubic pattern;that is, the formula for the sum of the squares of the first n integers is a cubic function,
We find a formula for the sum of the first n squares:Sn = 12 + 22 + 32 + 42+...+n2.We haveS1 = 1, S2 = 12 + 22 = 5, S3 = l2 + 22 + 32 = 14, S4 = 30, S5 = 55, S6 = 91.and so on. To make things a little simpler, we will also use the sum of the squares of the first zero terms , S0 = 02 = 0. Arranging these values in a table , we find thatSince the third differenes △3Sn are constant,the data values must follow a cubic pattern;that is, the formula for the sum of the squares of the first integers is a cubic function,