Find all values of x for which the geometric series 1+2(x-3)+4(x-3)[sup:tc6sc45w]2[/sup:tc6sc45w]+... converges
then, assuming these values for x, find S in terms of x.
Okay, so I know that if its going to converge the a/1-r can't be more than 1 but I can not quite figure out how the series. I thought it was 2n(x-3)[sup:tc6sc45w]n-1[/sup:tc6sc45w] but It can't be right becuase even if n is zero then the first term is 0 and then if its just n=1 it would make it zero again. I got confused, any help?
then, assuming these values for x, find S in terms of x.
Okay, so I know that if its going to converge the a/1-r can't be more than 1 but I can not quite figure out how the series. I thought it was 2n(x-3)[sup:tc6sc45w]n-1[/sup:tc6sc45w] but It can't be right becuase even if n is zero then the first term is 0 and then if its just n=1 it would make it zero again. I got confused, any help?
