Binomial expansions as infinite sums

Question 1

What happens if n on a binomial is negative?

what happens when r is bigger than n when n is positive?

here are some examples to illustrate:

Answer 1

Question 2

Some binomial expansions are only valid for certain values of x.

tell me how you work it out… you got to know this because you don’t know it hahahha. It’s actually easy look

Answer 2

Question 3

These kinds of questions they are a bit harder but you should be ok:

Answer 3