Y shud mod(x) be less than one in a binomial series?

Notice that ifx>1x>1, then the summation
1+x+x2+x3+…1+x+x2+x3+…
diverges to∞∞. And thus cannot be equal to a finite number.

in binomial series it goes till infinte terms if x is more than one then sum of series will be always infinity as when you increase power of a number that is more than one number increases thatwhy to get finite value x<1