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?

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- September 15th 2010, 09:30 PMDavyHilbertEpsilon Convergence Proof
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? - September 15th 2010, 10:50 PMProve It
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. - September 16th 2010, 08:14 AMDavyHilbert
We need to prove convergence by fixing ε > 0 and showing ε

- September 16th 2010, 08:35 AMDefunkt
1) You can simply write | | instead of absval, even with LaTeX.

2) As Prove It said,

Double click on the latex to see the correct code.