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

pardon my terrible latex skills

Find the limit of this series:

[itex]\sum[/itex] (n = 0 to ∞) (-1)[itex]^{n}[/itex]([itex]\frac{2}{3}[/itex])[itex]^{n}[/itex]

2. Relevant equations

No idea, it looks like an alternating series test, but I am supposed to actually find the sum, not just whether or not it converges.

3. The attempt at a solution

No idea

1. The problem statement, all variables and given/known data

[itex]\sum[/itex](k = 1 to ∞) [itex]\frac{(-1)^{k}k^{3}}{(1+i)^{k}}[/itex]

2. Relevant equations

3. The attempt at a solution

Once again, it looks like an alternating series. I tried the root test and got (1/2)-(1/2)i, but then I realized the root test is not applicable because the series is complex. No way to compare (1/2) - (1/2)i to the real number 1 in terms of ordering. Its not geometric so I don't have a formula for finding the sum.

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# Homework Help: 2 Complex Series problems

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