Ok

So I have the problem of:

A definition of a convergent infinite series with the sumis:S

Given any small positive number (ε) it possible to find an integeer N so that |S-Sn|<ε for everyn>N

Select some ε's and find the correspondingN's for the following series:

This is how far I got:

so

Let ε=1/8

Then |S-Sn|<1/8 for some n>N

so |1-Sn|<1/8

sn will always be positive and less than S ie less than 1 so

1-Sn<1/8

Sn>7/8

Now I am stuck... am I doing this right? If so how do I find N?

Any help appreachated.

colgon