Hi,
So right now I'm studying for an exam and I'm doing a problem on successions.
The problems asks whether
ln+1 - ln
is positive or negative.
ln = 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%5Cright)-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
So right now I'm studying for an exam and I'm doing a problem on successions.
The problems asks whether
ln+1 - ln
is positive or negative.
ln = 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%5Cright)-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