In the next formula, each term is half as large as the previous term.
Even when we don't know the exact number of terms, we can still say:
It may be somewhat surprising that the sum is less than 1 no matter how many terms there are. Figure C-3 shows why this is true.
Figure C-3. When the terms of a sum of halves are rearranged, they don't quite fill up a 2 x 1/2 rectangle. The missing piece is precisely the size of the last term: 1/2n.
It is sometimes more convenient to write a sum in which each term is twice (rather than half) the previous term.
C 5 Upper Limit on Sum of a Function
Part I: Object-Oriented Programming
Part II: Linear Structures
Stacks and Queues
Part III: Algorithms
Analysis of Algorithms
Searching and Sorting
Part IV: Trees and Sets
Part V: Advanced Topics
Advanced Linear Structures
Out to the Disk
Part VI: Appendices
A. Review of Java
B. Unified Modeling Language
C. Summation Formulae
D. Further Reading