# Math Help - Proof of that a limit -> 0 as n-> infinity

1. ## Proof of that a limit -> 0 as n-> infinity

Hey,

I've been trying to work out the following question,

This is it including what I hope is an ok, or on the way to an ok proof.

The book has a hint given that states there exists N in naturals such that |z_n|<ε/2 for all n>N so I kind of tried to use that to find a bound on w_n.

Does this look okay?

Jess

2. ## Re: Proof of that a limit -> 0 as n-> infinity

It is not true that for every ε there exists an N such that |zN+1+ ... +zₙ| < ε / 2 for all n > N. E.g., for zₙ = 1 / n, any tail zN+1 + zN+2 + ... is infinite.

It is even less true that |z₁ + ... + zN| < ε / 2. For example, we could have z₁ = 100.

sweet thanks