# Category:Summations

This category contains results about Summations.

Definitions specific to this category can be found in Definitions/Summations.

Let $R \left({j}\right)$ be a propositional function of $j$.

Then we can write the **summation** as:

- $\displaystyle \sum_{R \left({j}\right)} a_j = \text{ The sum of all $a_j$ such that $R \left({j}\right)$ holds}$.

If more than one propositional function is written under the summation sign, they must *all* hold.

## Subcategories

This category has the following 12 subcategories, out of 12 total.

### B

### E

### G

### N

### S

### T

## Pages in category "Summations"

The following 92 pages are in this category, out of 92 total.

### C

### E

- Exchange of Order of Indexed Summations
- Exchange of Order of Indexed Summations over Rectangular Domain
- Exchange of Order of Indexed Summations/Rectangular Domain
- Exchange of Order of Summation
- Exchange of Order of Summation with Dependency on Both Indices
- Exchange of Order of Summation with Dependency on Both Indices/Example
- Exchange of Order of Summation with Dependency on Both Indices/Infinite Series
- Exchange of Order of Summation with Dependency on Both Indices/Proof
- Exchange of Order of Summation/Example
- Exchange of Order of Summation/Finite and Infinite Series
- Exchange of Order of Summation/Infinite Series
- Exchange of Order of Summations over Finite Sets
- Exchange of Order of Summations over Finite Sets/Cartesian Product
- Exchange of Order of Summations over Finite Sets/Subset of Cartesian Product

### G

### I

- Indexed Summation does not Change under Permutation
- Indexed Summation of Multiple of Mapping
- Indexed Summation of Sum of Mappings
- Indexed Summation of Zero
- Indexed Summation over Adjacent Intervals
- Indexed Summation over Interval of Length One
- Indexed Summation over Interval of Length Two
- Indexed Summation over Translated Interval
- Indexed Summation without First Term

### P

### S

- Sum of Sequence as Summation of Difference of Adjacent Terms
- Sum of Summations equals Summation of Sum
- Sum of Summations equals Summation of Sum/Infinite Sequence
- Sum of Summations equals Summation of Sum/Infinite Sequence/Proof 1
- Sum of Summations equals Summation of Sum/Infinite Sequence/Proof 2
- Sum of Summations over Overlapping Domains
- Sum of Summations over Overlapping Domains/Infinite Series
- Sum of Zero over Finite Set
- Sum over Complement of Finite Set
- Sum over Disjoint Union of Finite Sets
- Sum over j of Function of Floor of mj over n
- Sum over j of Function of Floor of mj over n/Corollary
- Sum over k of Floor of Log base b of k
- Sum over k of Floor of Root k
- Sum over k of Sum over j of Floor of n + jb^k over b^k+1
- Sum over k of Sum over j of Floor of n + jb^k over b^k+1/Corollary
- Sum over Union of Finite Sets
- Summation by k of Product by r of x plus k minus r over Product by r less k of k minus r
- Summation by k of Product by r of x plus k minus r over Product by r less k of k minus r/Example
- Summation of General Logarithms
- Summation of i from 1 to n of Summation of j from 1 to i
- Summation of Multiple of Mapping on Finite Set
- Summation of Powers over Product of Differences
- Summation of Powers over Product of Differences/Example
- Summation of Product of Differences
- Summation of Products of n Numbers taken m at a time with Repetitions
- Summation of Sum of Mappings on Finite Set
- Summation of Summation over Divisors of Function of Two Variables
- Summation of Unity over Elements
- Summation of Zero
- Summation of Zero/Finite Set
- Summation of Zero/Indexed Summation
- Summation of Zero/Set
- Summation over Cartesian Product as Double Summation
- Summation over Finite Set Equals Summation over Support
- Summation over Finite Set is Well-Defined
- Summation over Interval equals Indexed Summation
- Summation over k of Ceiling of k over 2
- Summation over k of Ceiling of mk+x over n
- Summation over k of Floor of k over 2
- Summation over k of Floor of mk+x over n
- Summation over k of Floor of x plus k over y