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Give an analytic verification of Now, give a combinatorial

Chapter 1, Problem 17STE

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QUESTION:

Give an analytic verification of

               \(\left(\begin{array}{l}n \\2\end{array}\right)=\left(\begin{array}{l}k \\2\end{array}\right)+k(n-k)+\left(\begin{array}{c}n-k \\2\end{array}\right), \quad 1\leq k \leq n\)

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QUESTION:

Give an analytic verification of

               \(\left(\begin{array}{l}n \\2\end{array}\right)=\left(\begin{array}{l}k \\2\end{array}\right)+k(n-k)+\left(\begin{array}{c}n-k \\2\end{array}\right), \quad 1\leq k \leq n\)

ANSWER:

Step 1 of 2

From the given problem we have:

                                         

We need to give an analytic verification and a combinatorial argument for this identity.

 

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