n m
Σ Σ Xij
i=1 j=1
Hello, nassaufashionista!
What is the question?
$\displaystyle \displaystyle\sum^n_{i=1} \sum^m_{j=1}X_{ij}$
Are we expected to expand it?
$\displaystyle \displaystyle\sum^n_{i=1} \sum^m_{j=1}X_{ij} \;=\;\sum^n_{i=1}\big(X_{i1} + X_{i2} + X_{i3} + \cdots + X_{im}\big)$
. . . . . . . . $\displaystyle =\;\begin{Bmatrix}\;\;\;(X_{11} + X_{12} + X_{13} + \cdots + X_{1m}) \\ + (X_{21} + X_{22} + X_{23} + \cdots + X_{2m}) \\ + (X_{31} + X_{32} + X_{33} + \cdots + X_{2m}) \\ \vdots \qquad \qquad \vdots \qquad \qquad \vdots \\ + (X_{n1} + X_{n2} + X_{n3} + \cdots + X_{nm}) \end{Bmatrix}$
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.