 # How come ( n + 1 </mro Emely Baldwin 2022-05-23 Answered
How come ${\left(\frac{n+1}{n-1}\right)}^{n}={\left(1+\frac{2}{n-1}\right)}^{n}$?
I'm looking at one of my professor's calculus slides and in one of his proofs he uses the identity:
${\left(\frac{n+1}{n-1}\right)}^{n}={\left(1+\frac{2}{n-1}\right)}^{n}$
Except I don't see why that's the case. I tried different algebraic tricks and couldn't get it to that form.
What am I missing?
Thanks.
Edit: Thanks to everyone who answered. Is there an "I feel stupid" badge? I really should have seen this a mile a way.
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Just write
${\left(\frac{n+1}{n-1}\right)}^{n}={\left(\frac{n-1+2}{n-1}\right)}^{n}={\left(1+\frac{2}{n-1}\right)}^{n}$
###### Not exactly what you’re looking for? Nicholas Cruz
Note that
$\frac{n+1}{n-1}=\frac{n-1+2}{n-1}=\frac{n-1}{n-1}+\frac{2}{n-1}=1+\frac{2}{n-1}.$