# Math Help - Mathematical Inductions of Combinations

1. ## Mathematical Inductions of Combinations

If n is an integer and n > or = 2, prove recursively that the sum of the combinations C(J,2) from J=2 to N, is equal to the combination C(N+1, 3).

2. $C_2^2+C_3^2+C_4^2+\ldots+C_n^2=$

$=(\underbrace{C_3^3+C_3^2}_{C_4^3})+C_4^2+\ldots+C _n^2=$

$=(\underbrace{C_4^3+C_4^2}_{C_5^3})+\ldots+C_n^2=$

$\ldots\ldots\ldots\ldots\ldots$

$=C_n^3+C_n^2=C_{n+1}^3$