(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Does the series converge or diverge? Give reason for your answer; if it converges, find its sum.

[tex]\infty\sum[/tex] n=0 [tex]\frac{(-1)^{(n+1)} * 3 - 1}{2^n}[/tex]

2. Relevant equations

If |r|<1, the geometric series converges to a/(1-r). If |r|> or = 1, it diverges.

3. The attempt at a solution

[tex]\infty\sum[/tex] n=1 [tex]\frac{(-1)^{(n+1)} * 3}{2^n}[/tex] <---- This is a very similar problem that I was able to figure out.

In this problem, it's a geometric series that converges to 1 (with a sum of [tex]\frac{(3/2)}{1-(-1/2)}[/tex].

However, this particular problem has two differences. One is the -1 on top, which shouldn't matter as n-> infinity since it's so small. The other difference is it starts at zero, so I'm not sure if the above equation (in part "b") is relevant, with a/(1-r). I tried finding an "a" and got -4, but I'm not sure what to do about the r, besides assuming that the 3 and -1 don't matter:

Then I'd get (-1)^n+1 / 2^n which would be 1/2 = r. Help?

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# Homework Help: Series Convergence/Divergence Problem

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