Alternating sum of binomial coefficients for JEE

Formula

\[\sum_{r=0}^{n}(-1)^r{n\choose r}=0\quad (n\ge 1)\]

Variables: \(n\) is a positive integer.

Conditions: For \(n=0\), the sum equals \(1\).

Alternating coefficient sums via \((1-1)^n\), sign-based simplification.