Double summation

http://targetiit.com/iit_jee_forum/posts/gud_one_4300.html

I cant understand that :(

can some one explain double summations first i dont know anything of it

\sum_{0\leq r,s\leq n}^{}{\sum{f(r)(.)f(s)}} = \sum_{0\leq r<s\leq n}^{}{\sum{f(r)(.)f(s)}}+\sum_{0\leq r>s\leq n}^{}{\sum{f(r)(.)f(s)}} + \sum_{0\leq r=s\leq n}^{}{\sum{f(r)(.)f(s)}}

\sum_{0\leq r,s\leq n}^{}{\sum{f(r)(.)f(s)}} = 2\sum_{0\leq r<s\leq n}^{}{\sum{f(r)(.)f(s)}} + \sum_{0\leq r=s\leq n}^{}{\sum{f(r)(.)f(s)}}

2\sum_{0\leq r<s\leq n}^{}{\sum{f(r)(.)f(s)}}=\sum_{0\leq r,s\leq n}^{}{\sum{f(r)(.)f(s)}} - \sum_{0\leq r=s\leq n}^{}{\sum{f(r)(.)f(s)}}

use this for any sort of double summation functions and it makes the solution easy.

hope this makes it clear subash. :)

yep. it's in the same way i posted.

infact, Dead made it a question for test only after his forum discussion (link is given by manipal).! :)

done bfre ...