Prove that the sequence sum(i=1 --> n) 1/(10^i) converges.
I'm pretty sure it converges to 1/9 but how to we get there by fixing epsilon?
I'm not sure what you mean by "epsilon convergence" but this is a geometric series.
You should know that for a finite geometric series
.
Therefore it is convergent.
You should also be able to see that if you make , i.e. make this an infinite series, since , that means and thus the sum goes to , which is also convergent.