power series and permutation

Find the radius of convergence of the power series Sum of [(a_n)(x^n)] for the following choices of (a_n); n>=0.
i) a_(2n) = 0 and a_(2n+1) = n
ii) a_n = (m^n)^2 for some constant m E (0,inf)
(i.e E denotes "in the interval of")

Write the following permutations of the set {1,2,3,4,5,6,7,8} in cyclic form, and the express them as composites of transpositions, and hence decide whether they are even or odd permutations.
i) 1->8, 2->1, 3->4, 4->7, 5->5, 6->3, 7->2, 8->6
ii) 1->6, 2->8, 3->3, 4->4, 5->2, 6->1, 7->7, 8->5
iii) 1->1, 2->6, 3->5, 4->4, 5->8, 6->7, 7->2, 8->3