# do you know the properties of summation

• Nov 7th 2008, 07:23 AM
pandakrap
do you know the properties of summation
if you multiply two summation notation
ex.

(summation (x)) *(summation(y)) do you get (sumation (xy)) ??
• Nov 7th 2008, 07:33 AM
Moo
Hello,
Quote:

Originally Posted by pandakrap
if you multiply two summation notation
ex.

(summation (x)) *(summation(y)) do you get (sumation (xy)) ??

Is $(a+b)*(c+d)$ equal to $ac+bd$ ?
• Nov 7th 2008, 07:35 AM
pandakrap
no. it = ac + cd + ad + bd
• Nov 7th 2008, 07:47 AM
Moo
Quote:

Originally Posted by pandakrap
no. it = ac + cd + ad + bd

So try :
$\left(\sum_{i=1}^2 a_i \right) \times \left(\sum_{i=1}^2 b_i \right)=(a_1+a_2) \times (b_1+b_2)$

$\sum_{i=1}^2 a_i b_i=a_1b_1+a_2b_2$

is $(a_1+a_2) \times (b_1+b_2)$ equal to $a_1b_1+a_2b_2$ ?
And hence is your formula correct ?

You can see here : Cauchy product - Wikipedia, the free encyclopedia for the formula of the product of two summations ;)