# double summations:

• Jan 20th 2013, 05:58 AM
nassaufashionista
double summations:
n m
Σ Σ Xij
i=1 j=1
• Jan 20th 2013, 06:46 AM
Soroban
Re: double summations:
Hello, nassaufashionista!

What is the question?

Quote:

$\displaystyle \displaystyle\sum^n_{i=1} \sum^m_{j=1}X_{ij}$

Are we expected to expand it?

$\displaystyle \displaystyle\sum^n_{i=1} \sum^m_{j=1}X_{ij} \;=\;\sum^n_{i=1}\big(X_{i1} + X_{i2} + X_{i3} + \cdots + X_{im}\big)$

. . . . . . . . $\displaystyle =\;\begin{Bmatrix}\;\;\;(X_{11} + X_{12} + X_{13} + \cdots + X_{1m}) \\ + (X_{21} + X_{22} + X_{23} + \cdots + X_{2m}) \\ + (X_{31} + X_{32} + X_{33} + \cdots + X_{2m}) \\ \vdots \qquad \qquad \vdots \qquad \qquad \vdots \\ + (X_{n1} + X_{n2} + X_{n3} + \cdots + X_{nm}) \end{Bmatrix}$
• Jan 21st 2013, 01:43 AM
nassaufashionista
Re: double summations:
Ok Thank you! i was looking at another double summation:

2 3
Σ Σ Xij
i=1 j=1

The expansion in my text is as follows:
(x11+x12+{x13}+x21+x22+x23
^i dont understand why the x13 is used because i is only 1 to 2...
can you explain the x13 in parenthesis and explain the expansion I think i may have missed something.