Mathematics

The key is recognizing that $\ln(1-3x)$ is just $\ln(1+u)$ where $u = -3x$. Since the original series converges when $|u| < 1$, you need to substitute and solve for the constraint on $x$. This transforms a convergence problem into a simple inequality about the argument inside the logarithm.

The key is recognizing that $\ln(1-3x)$ is just $\ln(1+u)$ where $u = -3x$. Since the original series converges when $|u| < 1$, you need to substitute and solve for the constraint on $x$. This transforms a convergence problem into a simple inequality about the argument inside the logarithm.