- #1
MathematicalPhysicist
Gold Member
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- 371
i have to prove that:
n
sum [C(n,k)]^2=C(2n,n)
k=0
i have in my text a hint that i need to use:
(1+x)^n(1+x)^n=(1+x)^2n
but i got that:
n 2n
sum [C(n,k)]^2= sum [C(2n,k)]
k=0 k=0
how do i get out of this mess?
n
sum [C(n,k)]^2=C(2n,n)
k=0
i have in my text a hint that i need to use:
(1+x)^n(1+x)^n=(1+x)^2n
but i got that:
n 2n
sum [C(n,k)]^2= sum [C(2n,k)]
k=0 k=0
how do i get out of this mess?