Finite Alternative Odd Power Series
(Posted on October 15, 2006)
The sums of the following expressions are true for any positive integer n.
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Example:
Let n = 3, the left-hand side of the above expression is 1-3+5 = 3 and its right-hand side is –3(-1) = 3.
2. 
Example:
Let n = 3, the left-hand side of the above expression is 1-9+25 = 17 and its right-hand side is –2(9)(-1) –1 = 17.
3. 
Example:
Let n = 4, the left-hand side of the above expression is 1-27+125-343 = -244 and its right-hand side is [3(4) – 4(64)](1) = -244.
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