How do we expand binomial expressions when n is not an integer, for example $\displaystyle \sqrt{1+x}$?
If you have $\displaystyle \sqrt{1+x}$ as your exponent, e.g., $\displaystyle (a+b)^{\sqrt{1+x}}$, then you won't be using binomial expansion. Perhaps you're supposed to use logarithms.
Edit: Seems I misinterpreted your question. At any rate, maybe this link on Newton's generalized binomial theorem will help.
Sorry. It was my fault. I should have worded it better.
Got it! Thank you. Little bit got confused about as to what $\displaystyle \frac{(r)_k}{k!}$ meant initially but got it. Thanks again.At any rate, maybe this link on Newton's generalized binomial theorem will help.