- #1
utleysthrow
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Homework Statement
Prove whether [tex]\sum \frac{1}{ln(e^{n}+e^{-n})}[/tex] converges or diverges
Homework Equations
The Attempt at a Solution
(second post today... sorry, I just want to make sure I'm getting this right)
Since [tex]e^{n}+e^{-n}[/tex] goes to infinity as n goes to infinity, could I say that [tex]\sum \frac{1}{ln(e^{n}+e^{-n})}[/tex] is like [tex]\sum \frac{1}{ln(n)}[/tex]?
I know that [tex]\sum \frac{1}{ln(n)}[/tex] is definitely divergent because it is > 1/n and I can use the comparison test.
But could I argue that [tex]\sum \frac{1}{ln(e^{n}+e^{-n})}[/tex] and [tex]\sum \frac{1}{ln(n)}[/tex] are essentially the same?