Find the radius of convergence, R, of the series. Voxn + 6 n = 1 R = X Find the interval, I, of convergence of the series. (Enter your answer using interval notation.) I = XEXAMPLE 1 For what values of x is the series n!x3n convergent? n = 0 SOLUTION We use the Ratio Test. If we let an, as usual, denote the nth term of the series, then an = n!x30. If X # 0, we have lim an + 1 = lim n -00 an n - co X n!xin = lim = n - 00 X X By the Ratio Test, the series diverges when x * 0. Thus the given series converges only when X = 0Find a power series representation for the function. f(x) = arcta n(%) x Z x n=0 Determine the radius of convergence, R. R = a Need Help? \fUse a Maclaurin series in this table to obtain the Maclaurin series for the given function. f(x) = 9x cos 8 n = 0 X Need Help? Read It Watch It Master It