Give an example of such a convergent series

[gas8]

Homework Statement

Give an example of a convergent series $$\Sigma$$ z$$_{n}$$

So that for each n in N we have:

limsup $$abs{\frac{z_{n+1}}{z_{n}}}$$ is greater than 1

 

[Dick]

How about combining the convergent series 2^(-n) and 3^(-n) in a clever way? Hint: alternate terms from each.

 

[gas8]

yeah thx, I used 2^(-n) when n is even and 2^-(n+1 ) when n is odd

 

[Dick]

yeah thx, I used 2^(-n) when n is even and 2^-(n+1 ) when n is odd

Something like that will work, but doesn't that just give you limsup=1?