double summation

• April 26th 2009, 07:32 PM
jlt1209
double summation
(sorry i dont know how to do the summation symbol)

double summation, j=1 to 4 and k=2 to 8 (j*k)

is there a specific formula you are supposed to use?
• April 28th 2009, 02:16 AM
Moo
Hello,
Quote:

Originally Posted by jlt1209
(sorry i dont know how to do the summation symbol)

double summation, j=1 to 4 and k=2 to 8 (j*k)

is there a specific formula you are supposed to use?

$\sum_{j=1}^4 \sum_{k=2}^8 jk=\sum_{j=1}^4 \left( \sum_{k=2}^8 jk\right)$
In the second summation, since j doesn't depend on k, you can get it out from the sum :
$=\sum_{j=1}^4 \left(k \sum_{j=1}^8 j\right)$

You can calculate the sum $\sum_{j=1}^8 j$, by using this known formula : $\sum_{k=1}^n k=\frac{n(n+1)}{2}$

And then, you're left with only one sum, that should be easy to compute ;)
• April 28th 2009, 09:15 PM
matheagle
$\sum_{j=1}^4 \sum_{k=2}^8 jk=\sum_{j=1}^4 \left( \sum_{k=2}^8 jk\right)$
$=\left(\sum_{j=1}^4 j\right)\left(\sum_{k=2}^8 k\right)$
$=\left(\sum_{k=2}^8 k\right)\left(\sum_{j=1}^4 j\right)$