If n=m2, then the value of n2 is given by:

Question

If $n=\binom{m}{2}$, then the value of $\binom{n}{2}$ is given by:

Accepted Answer

$n = \dfrac{m(m-1)}{2}$

$$\binom{n}{2} = \frac{n(n-1)}{2} = \frac{m(m-1)\left[\frac{m(m-1)}{2}-1\right]}{4} = \frac{m(m-1)(m^2-m-2)}{8}$$
$$= \frac{m(m-1)(m-2)(m+1)}{8} = \frac{3(m+1)m(m-1)(m-2)}{24} = 3\binom{m+1}{4}$$

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