differentiate mathematically, between resistances in series and in parrallel

Answer 1

Hope this will give you a kick-start.
http://en.wikipedia.org/wiki/Series_and_parallel_circuits
http://www.kpsec.freeuk.com/resistan.htm

There is a lot of material you can obtain to help you complete your article.
Try Googling:
"resistance parallel series"
or other keywords.

Answer 2

If R1 and R2 be the two resistances connected in
(a)series, then equivalent resistance=R1+R2
(b)parallel, then equivalent resistance=(R1*R2)/(R1+R2)