Some Mathematical Aids

Jiuping Xu () and Liming Yao ()
Additional contact information
Jiuping Xu: Sichuan University
Liming Yao: Sichuan University

Chapter Appendix A in Random-Like Multiple Objective Decision Making, 2011, pp 397-401 from Springer

Abstract: Abstract Geometric series: From $$(1 - r)(1 + r + {r}^{2} + \cdots+ {r}^{n}) = 1 - {r}^{n+1}$$ , we obtain $$\begin{array}{rcl} {\sum\nolimits }_{k=0}^{n}{r}^{k} = \frac{1 - {r}^{n+1}} {1 - r},\ {\it { for}}\ r\neq 1.& & \\ \end{array}$$

Date: 2011
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:lnechp:978-3-642-18000-2_7

Ordering information: This item can be ordered from
http://www.springer.com/9783642180002

DOI: 10.1007/978-3-642-18000-2_7

Access Statistics for this chapter

More chapters in Lecture Notes in Economics and Mathematical Systems from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().