- #1
DPMachine
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Homework Statement
Give an example of a sequence [tex](a_n)[/tex] so that [tex]lim_{n\rightarrow\infty} \left|a_{n+1}/a_{n}\right| =1[/tex] and [tex]\sum^{\infty}_{n=1} a_{n}[/tex] converges
Homework Equations
(Maybe relevant, maybe not)
Theorem which states:
If [tex]\sum^{\infty}_{n=1} a_{n}[/tex] converges, then [tex]lim_{n\rightarrow\infty} a_{n} =0[/tex]
The Attempt at a Solution
I'm having trouble coming up with [tex]\sum^{\infty}_{n=1} a_{n}[/tex] that converges...
Since [tex]lim_{n\rightarrow\infty} a_{n} =0[/tex] doesn't imply the convergence of [tex]\sum^{\infty}_{n=1} a_{n}[/tex] (the theorem only works the other way around), I'm not sure where to start.
Any hint will be appreciated. Thank you.