1. ## Series convergence test

The problem is asking to prove that the series either converges or diverges. I think I know how to prove divergence but I need someone to confirm. The series is the sum from 1 to infinity of:

$\displaystyle (2^(n-1)+1)/2^n$

Given that the sum does diverge (right?), you can simplify and say that the original problem, for all values of N > 1, is greater than $\displaystyle (2^(n-1))/2^n.$ Since that equation always yields a value a 1/2, the sum diverges, and since the original sum is greater than that, it must diverge too. Is everything correct?

2. Originally Posted by Tbone456
The problem is asking to prove that the series either converges or diverges. I think I know how to prove divergence but I need someone to confirm. The series is the sum from 1 to infinity of:

(2^(n-1)+1)/2^n

Given that the sum does diverge (right?), you can simplify and say that the original problem, for all values of N > 1, is greater than $\displaystyle (2^(n-1))/2^n.$ Since that equation always yields a value a 1/2, the sum diverges, and since the original sum is greater than that, it must diverge too. Is everything correct?
Yes