Posted by **Isaac** on Friday, July 26, 2013 at 11:23pm.

How can I prove this series alternating series converges(this is the answer)?

(-1)^2*(2/3)^n

I tried it this way: an = (2/3)^n, then i just broke it down. 2^n/(3^n) and i took the ratio of it and got 2/3 which does not equal to one which would mean the series diverges.. but that's obviously not how its done i guess

- Calculus -
**Steve**, Saturday, July 27, 2013 at 12:01am
I assume you mean

(-1)^n * (2/3)^n

This is just a geometric series with r = -2/3

So, if you start with n=0, the sequence starts with 1, and

Sum = 1/(1-r) = 1/(1+2/3) = 3/5

In an alternating series, if the ratio |r| < 1 it converges.

## Answer this Question

## Related Questions

- Calculus - If you have a geometric alternating series, and you prove that the ...
- Calc - Does 1/ln(x+1) converge or diverge? I've tried the nth term test, limit ...
- Calculus - Determine the following about the series. Indicate the test that was ...
- Calculus - a) Find the Taylor series associated to f(x) = x^-2 at a = 1. Be sure...
- calculus - test the series for convergence or divergence using the alternating ...
- calculus - test the series for convergence or divergence using the alternating ...
- math - test the series for convergence or divergence using the alternating ...
- Calculus - I'm studying infinite series and am really struggling with memorizing...
- calc. - find the sum of the series of (-2)^n/3^n+1. This is an alternating ...
- calculus - With power series, is an endpoint convergent if you plug it back into...

More Related Questions