1. The problem statement, all variables and given/known data Verify that the infinite series diverges. I have the series from n=1 to infinity of (2^(n)+1/2^(n+1) 2. Relevant equations Nth term test(This is the way the book did it but I did it used the geometric series test and I just want to verify if my Algebra was correct) 3. The attempt at a solution First I split the series into two separate series and let the series go from n=0 to infinity. So I have 2^(n+1)/2^(n+2) add 1/2^(n+2). I believe I can then bring down the some of the exponents and simplify to 2*2^n/4*2^n add 1/4*2^n so for the first series I let a=1/2 and r=1^n because |r|=|1| is greater than or equal to 1, the series diverges. I completely ignored the second series that I made because its irrelevant to simplify as I already know the first series diverges. Is this proof valid and was my algebra correct?