Convergence or Divergence of a Geometric Series with r= 1/10

[Punchlinegirl]

Evaluate \Sigma 2(1/10)^n or explain why it diverges. (Infinity is on the top of the sum and n=1 on the bottom, I just didn't know how to put it in latex)

This was a test question that I got wrong. I thought that it was a geometric series with r= 1/10. This would mean that r is less than 1 so the series would converge. Why is the question saying that it will diverge?

 

[SpaceTiger]

Why is the question saying that it will diverge?

It's not, it's saying to either evaluate it or explain why it diverges. If it just told you to evaluate it, then it would be telling you that the series converges. They want you to figure that out for yourself. Far as I can tell, that's a converging series with a value of 2/9.

 

[dextercioby]

I get \frac{2}{9},too.It would have been \frac{20}{9},had the summation started from n=0.

To the OP:

\sum_{n=1}^{\infty} \frac{2}{10^{n}}


Daniel.