1^3 - 2^3 + 3^3 -...+ n^3

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Adding Sequences In The Form: 13 - 23 + 33 -...+ n3

A.  In adding sequences of this nature there are two possibilities:

1.  n is odd

2.  n is even

B.  If n is odd then use the formula:

a2(4a-3), where a=(n+1)/2

C.  If n is even then use the formula:

- a2(4a+3), where a = n/2

D.  Examples

Ex [1]  13 - 23 + 33 - 43 + 53 = _________

a.  In this case a = 3, since 5+1/2 = 3.

b.  So since 5 is odd, we use 32(4(3)-3) = 9(9) = 81.

c.  The answer is 81.

Ex [2]  (63 + 43 + 23) - (53 + 33 + 13) = ____

a.  In this case, the problem is switched where the odds are negative which only negates the negative from our equation.

b.  a = 3, since 6/2 = 3.

c.  So, 32(4(3)+3) = 9(15) = 135.

d.  The answer is 135.

 

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