Problem 1164 (difficulty: 1/10)

By the binomial theorem \(\displaystyle \displaystyle (1+x)^\alpha = \sum_{k=0}^\infty \binom{\alpha}{k} x^k\) if \(\displaystyle |x|<1\). Which identities result in the \(\displaystyle \alpha=-1\) and \(\displaystyle \alpha=-2\) cases?

Give me another random problem!