binomial Sum.

[jagdish]

Calculate sum of $\bf ^nC_{0}-^{n-1}C_{1}+^{n-2}C_{2}-^{n-3}C_{3}..................$

[Moon]

Misunderstood the problem!

\[(1-x)^n=\sum_{i=0}^n (-1)^i\binom{n}{i} x^i\]
Setting $x=1$, we get,\[\sum_{i=0}^n (-1)^i\binom{n}{i} =(1-1)^n=0\]

I'll be back with a solution!

[rakeen]

hey, is there really is a result for this infitive series?

[*Mahi*]

Calculate sum of $\bf ^nC_{0}-^{n-1}C_{1}+^{n-2}C_{2}-^{n-3}C_{3}..................$

Hey ,I think for any $n$ this series $n,n-1,n-2,....$ will end and thus this is not an infinite sequence(as long as you are not thinking about things like ${^{-3}}C_5$),they do exist,but extremely tough(includes falling factor),and I think this is not a wise idea to discuss things this hard in a forum!