EXAMPLE 5 Test the convergence of the series na n! n = 1 SOLUTION Since the terms an = n"/n! are positive, we don't need the absolute value signs. (n + 1)"+1.n! an (n + 1)! nn an + 1 (n + 1)" n! = (n + 1)n! n n n + 1 1 + as n 00 n n Since e > 1, the given series is divergent by the Ratio Test. EXAMPLE 6 Test the convergence of the series 7n + 4 12n + 2 n=1 SOLUTION n 7n + 4 12n + 2 lan! 7 + 4 n <1 12 + 2 Thus the given series converges by the Root Test.
