Question

Expand each. $$ \sum_{j=1}^{2} \sum_{i=1}^{3} a_{i j} $$

   Expand each.
$$
\sum_{j=1}^{2} \sum_{i=1}^{3} a_{i j}
$$

Discrete Mathematics with Applications

Discrete Mathematics with Applications

Thomas Koshy 1st Edition

Chapter 3, Problem 50

Instant Answer

Solved by Expert Mohamed Mohamed

10/05/2021

Step 1

The inner summation is over i which runs from 1 to 3, and the outer summation is over j which runs from 1 to 2. Show more…

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Expand each. $$ \sum_{j=1}^{2} \sum_{i=1}^{3} a_{i j} $$

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Key Concepts

Order of Summation

An important aspect of double or nested sums that specifies that the summation should be performed in a specific sequence, usually starting with the inner summation and then proceeding to the outer summation. This ordering helps to systematically account for all terms in the overall sum.

Summation Notation

A compact way to represent the addition of a sequence of values using the ? (sigma) symbol. It typically involves specifying an index that runs over a set of integers and an expression whose values are added together as the index changes.

Double Summation

A method used to compute the sum over two indices, where one summation is nested inside another. In a double summation, the inner sum is evaluated for each fixed value of the outer index, and the results are then summed according to the outer index's limits.

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