# summation and product rules

• Apr 26th 2009, 01:12 PM
revolution2000
summation and product rules
I am struggling with the basic theory behind summations and products of the series of numbers can anybody give me a link to a site with some theory or give me some general rules.

Example

log(product series from i = 1 to n of ((lambda ^xi)/xi!)

= summation from i = 1 to n of (xi * log lambda - log (xi!))

how do you get from the product of the numbers to the summation?????
• Apr 26th 2009, 01:23 PM
Plato
Quote:

Originally Posted by revolution2000
I am struggling with the basic theory behind summations and products of the series of numbers can anybody give me a link to a site with some theory or give me some general rules.

Example

log(product series from i = 1 to n of ((lambda ^xi)/xi!)

= summation from i = 1 to n of (xi * log lambda - log (xi!))

how do you get from the product of the numbers to the summation?????

$\log(a\cdot b\cdot c)=\log(a)+\log(b)+\log(c)$
$\log \left( {\prod\limits_{k = }^N {x_k } } \right) = \sum\limits_{k = 1}^N {\log \left( {x_k } \right)}$