Hi,

So right now I'm studying for an exam and I'm doing a problem on successions.

The problems asks whether

l_{n+1 }- l_{n }is positive or negative.

l_{n}= 1/(2^(n-3))

I was able to solve most of it, but then I got stuck; so I looked up a solution in symbolab:

https://www.symbolab.com/solver/polynomial-equation-calculator/%5Cfrac%7B1%7D%7B2%5E%7B%5E%7B%5Cleft(n%2B1%5Crigh t)-3%7D%7D%7D-%5Cfrac%7B1%7D%7B2%5E%7B%5E%7Bn-3%7D%7D%7D

The part that I don't understand about this solution is from here forward (in the nominator):

2^(^(n-3))-2^(^{n-2))

where the website factors out the common term 2^(-3)*2^n of

2^(^(n-3))-2^(^{n-2))

to get

-2^(n-3)

Can someone help me understand this factoring? I'm confused by how the site got to this final answer. How does it factor out 2^(-3)*2^n ?

If you can help me understand this I would really appreciate it.

P.S. Sorry if the formatting is horrible. I'm still figuring out how to use the site

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