Finite Alternative Odd Power Sum
Submitted by admin on Tue, 03/17/2009 - 11:15am
Finite Alternative Odd Power Sum
(October 15, 2006)
The sums of the following expressions are true for any positive integer n.
1. 
.
.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.
4. 
.
.5. 
.
.6. 
.
.7. 
.
.8. 
.
.9. 
.
.10. 
.
.11. 
.
.12. 
.13. 
.14. 
.15. 
.16. 
.17. 
.18. 
.
Other finite series:
- Finite Power Sum
- Finite Odd Power Sum
- Repeated Power Sum
- Sum Of Partial Factorials
- Some Finite Series Found in Closed-Form
In-Text or Website Citation
Tue N. Vu, Finite Alternative Odd Power Sum, 10/15/2006, from Series Math Study Resource.
Hyperlink: http://www.seriesmathstudy.com/finitealternativeodd.
Hyperlink: http://www.seriesmathstudy.com/finitealternativeodd.
| A mathematical truth is neither simple nor complicated in itself, it is. | |
| Emile Lemoine |
