An infinite geometric series has first term 6 and positive common ratio r. The sum to infinity is known to be 15.
a. (i) Show that r satisfies the equation 1−r6=15.
b. (ii) Solve the equation obtained in part (i) to find all possible values of r.
c. (iii) From the values found in part (ii), identify the one that actually gives a convergent series and state a brief reason for your choice.