# Convergent and divergent series?

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• June 2nd 2011, 01:22 PM
homeylova223
Convergent and divergent series?
Use the ratio test to determine whether each series is convergent or divergent.

1. (4/3)+(4/9)+(4/27)+(4/81)

2. 2+(4/2^2)+(8/3^2)+(16/4^2)

Well my issue on this problem is finding the (An) as my book calls it so that I can actually do the ration test.

for number one I know it 4/(n something but I am confused what function would express the series) I though it was (n)^3 but that wont work.

for number 2 I know it is n/n^2 but I am not sure how to represent the numerator.
• June 2nd 2011, 01:31 PM
TKHunny
Well, you WILL need to do better than that.

1. $\frac{4}{3^{1}} + \frac{4}{3^{2}} + \frac{4}{3^{3}} + \frac{4}{3^{4}} + ...$

2. $\frac{2^{1}}{1^{2}} + \frac{2^{2}}{2^{2}} + \frac{2^{3}}{3^{2}} + \frac{2^{4}}{4^{2}} + ...$

You write the nth term.