Find the values of x for which the power series 3 + 3(4x+1) + 3(4x+1)^2 + 3(4x+1)^3 + ...+ converges?

Question

Is it -1/2 < x < 0

Answer 1

The power series converges when

| 4x + 1| &lt; 1

or -1 &lt; 4x +1 &lt; 1

or -2 &lt; 4x&lt; 0

or -1/2 &lt; x &lt; 0

so your range is proper