My book mentioned that
"If -1<x<1, then (1+x)^n = 1 + nx + n(n-1)(x^2)/2! + n(n-1)(n-2)(x^3)/3! + ... + n(n-1)(n-2)...(n-r+1)(x^r)/r! + ..."
Why -1<x<1? Why is this restriction on x necessary?
Thanks in advance.
The series depends on x. But the series itself is only convergent if it follows specific conditions, which means that it will only be convergent for particular values of x (the ones which will satisfy the conditions). I suggest you research convergence tests for infinite series.
The OP was actually referring to the GENERALISED Binomial Theorem, which is an infinite series.