Question

using mathematical induction, prove that for all positive integers n the following equation holds true

Summation from t=0 to (n-1) : (n choose i)(-1)^(i+1)=(-1)^n

Answer 1

\[\sum_{i=0}^{n-1}\left(\begin{matrix}n \\ i\end{matrix}\right)(-1)^{i+1}=(-1)^{n}\]