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mathnoobie
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Homework Statement
Verify that the infinite series diverges.
I have the series from n=1 to infinity of (2^(n)+1/2^(n+1)
Homework 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)
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?