Show that if $n$ is a positive integer, then $C(2n, 2) = 2C(n, 2) + n^2$.
Added by Jordi R.
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Step 1
Let's plug in the expressions we found above: (2n)! / (2!(2n-2)!) = 2(n! / (2!(n-2)!)) + n^2 Now, let's simplify the equation: (2n)! / (2!(2n-2)!) = 2(n! / (2!(n-2)!)) + n^2 (2n)! = 2(n!)(2n-2)! + n^2(2!(2n-2)!) Now, let's use the property that (2n)! = Show more…
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