double summation

**jlt1209** · April 26th 2009, 07:32 PM

(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?

**Moo** · April 28th 2009, 02:16 AM

Hello,

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

**matheagle** · April 28th 2009, 09:15 PM

Typo alert.....

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

or

$=\left(\sum_{k=2}^8 k\right)\left(\sum_{j=1}^4 j\right)$

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