Vandermonde's identity

• binomial coefficient formula
• ${\sum }_{i=0}^k\left(\genfrac{}{}{0ex}{}{n}{i}\right)\left(\genfrac{}{}{0ex}{}{m}{k-i}\right)=\left(\genfrac{}{}{0ex}{}{n+m}{k}\right)$
  • [Number of routes
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• Proof of Van der Mond’s convolution in three different ways | A beautiful story in high school math
• special case(k=n, m=n)
  • ${\sum }_{i=0}^n{\left(\genfrac{}{}{0ex}{}{n}{i}\right)}^2=\left(\genfrac{}{}{0ex}{}{2n}{n}\right)$

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