Posted by Lucy on .
Which of the following series is divergent?
a) 1+3(1/4)+9(1/4)^2+27(1/4)^3...
b) 1+3(1/5)+9(1/5)^2+27(1/5)^3...
c) 1+3(1/7)+9(1/7)^2+27(1/7)^3...
d) 1+3(1/2)+9(1/2)^2+27(1/2)^3...
How do you determine if a series in convergent or divergent???
The book that I have is about as clear as mud and I do not understand...
Thanks for your help!!

Precalculus 
Reiny,
This would be a lengthy reply, so see if you can make sense out of this
http://faculty.msmary.edu/heinold/m248spring2007/m248spring2007_convergence_tests.pdf
I will take a look at the first question
1+3(1/4)+9(1/4)^2+27(1/4)^3...
= 1 + 3^1 / 4^1 + 3^2 / 4^2 + ..
= 1 + summation of (3/4)^n as n goes from 1 to infinitity
Now compare this result with what it says about the summation of a geometric series at the top of the link I gave you.
good luck.