answer in detail

Question 8 Suppose that {an} is a sequence of positive numbers with lim, too Van = r, where r is a real number. If E 3" an converges, then (a) r = 1/3 (b) r 1/3 (d) r>3 (e) none of these Question 9 If the radius of convergence of Cake" is 1, then the series Cak(2x - 1)* converges when a belongs to (a) (-3, 1) (b) (-3, 3) (c) (0, 1) (d) (-2, 4) (e) none of these Question 10 Suppose that the series _ ax5* converges. Then > (-;)" (a) converges conditionally (b) converges absolutely (c) diverges (d) has radius of convergence equals to 5 (e) none of these