Two infinite geometric series S1 and S2 satisfy the following information.
• The first term of S1 is 10 and its common ratio is 31.
• The ratio of the sums to infinity is S1:S2=3:2.
• The first term of S2 is 4.
Answer the following questions.
a. (i) Find the sum to infinity of S1.
b. (ii) Using the given ratio of sums, determine the exact value of the sum to infinity of S2.
c. (iii) Hence find the common ratio of S2.
d. (iv) Verify whether S2 converges with the common ratio obtained in part (iii).