Find the radius of convergence for the power series (2x/3)^n from n= 0 to infinity?

Answer 1

Sum_(n=0 to oo) a^n convergent when |a| <1

=>
|2x/3| < 1
or
-1<2x/3<1
-3/2 < x < 3/2

Answer 2

This is a geometric series with r=2x/3
so if
-1<2x/3<1 the series is convergent
-3/2

Answer 3

there is an x^n and a (-a million)^n interior the numerator and there is basically an (n + a million) interior the denominator, precise? if so, the series converges for -a million < x <= a million and its radius of convergence is a million.