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You can just rewrite \((-2)^{n}=2^{n}*(-1)^{n}\)

Do you know the alternating series test?

It has to satisfy that an+1<= an and lim an = 0

in order to be convergent

Are you having trouble on finding \(b_{n}\)?

is bn just 2^n/7^n

What about the n?

I mean, there's a n multiplying what you just posted.

Oh right my bad so bn=n2^n / 7^n right?

yes. You can just write that as \(n*(\frac{2}{7})^{n}\)

Can you finish it?

I am having troubles finding the limit. can i just use l'hopitals rule?

Ah yes 7^n grows much faster than n*2^n therefore the limit is zero.

Yes. You might try doing the limit though.

I would use the first derivative test on bn. to See if it eventually decreases

You can now finish the question without problems.

If i took the absolute value of an |an| = would i get n*2^n/7^n

Yes.

But you just need to check the limit and if the sequence \(b_{n}\) decreases really.

Oh okay. thanks!

Oh, right, we need to check for absolute convergence!

I missed that. But it seems you got it.

So by taking the absolute value it would no longer be an alternating series?

Yes. By taking |an| you check for absolute convergence.