



The
p Series 


The
other basic type of series is called the p Series. 


It
looks like this ... 








"p"
is just some constant.






Notice
that with this one we start with n = 1, not n = 0. 


Notice
also that we show n in a denominator. 


The
deal is, if n is in the numerator, the number will be bigger than 1. 


Adding
up a bunch of these to ANY exponent greater than 0 will go to
infinity 


so
those are kind of nobrainers. 


Notice
also that since the numerator is 1, 


showing
the exponent on the denominator or the whole fraction 


is
really the same thing. 


That
is ... 











Some
examples of this kind of series are ... 














This
type of series adds up to a number if p > 1. 


The
p series looks a lot like a geometric series. 


Ones
that converge to a number look really similar. 


But
they are really two different things. 











The
difference gets important when you calculate 


the
number to which the p Series totals. 


The
value of a p Series is totaled in a completely different way. 





What
we use is an integral. 


So
for the last p series ... 











You
can change the n to an X if it makes you feel better. 











We
could have used an integral on the geometric example too, 


but
the formula we did use is much easier. 





copyright 2005 Bruce Kirkpatrick 
