Solution to Show that C (n+1, k) = C (n, k -1) + C (n, k) - Sikademy
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Show that C (n+1, k) = C (n, k -1) + C (n, k)

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Here's the Solution to this Question

C(n,k-1)=\dbinom{n}{k-1}=\dfrac{n!}{(k-1)!(n-k+1)!}

C(n,k)=\dbinom{n}{k}=\dfrac{n!}{k!(n-k)!}

Then


C(n,k-1)+C(n,k)

=\dfrac{n!}{(k-1)!(n-k+1)!}+\dfrac{n!}{k!(n-k)!}

=\dfrac{n!(k+n-k+1)}{k!(n-k+1)!}=\dfrac{n!(n+1)}{k!(n-k+1)!}

=\dfrac{(n+1)!}{k!(n+1-k)!}=C(n+1,k)



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Question ID: mtid-5-stid-8-sqid-1272-qpid-1010