1.      Find the radius of convergence of each of the following power series

a)     

b) 

c) 

d) 

e) 

f) 

g) 

h)

2.       Find the radius of convergence of each of the following power series

a) 

b) 

c) 

d) 

e) 

3.      a)  Let A be the set of limits of all subsequences of a given sequence   prove that

b)      Show that

==L.

4.      Let   Let be a sequence of positive terms converging to a limit v.

Show that

a)

b) where is a sequence of positive terms.