how come when u multiply a series by x^n or when u multiply a series by a constant, it doesnt change the radius of convergence? ex: the power series representation for e^x, the ROC doesnt change for the series represenation of x^2e^x, or if a constant was multiplied to the series represenation for e^x, i know that if u use the ratio test it's true that the ROC doesnt change, but like can someone explain to me like why intuitively it would be true?