Series

[gas8]

1. The problem statement, all variables and given/known data

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?