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23-06-2017
Mathematics

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Give an algebraic proof that 2n choose 2 = 2 (n choose 2) +n^2

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LammettHash LammettHash

23-06-2017

[tex]\dbinom{2n}2=\dfrac{(2n!)}{2!(2n-2)!}=\dfrac{2n(2n-1)}2=n(2n-1)=2n^2-n[/tex]

[tex]2\dbinom n2+n^2=2\dfrac{n!}{2!(n-2)!}+n^2=n(n-1)+n^2=2n^2-n[/tex]

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