Binomial fun

Probability Level 2

Consider the binomial expansion:

(1+x)n=C0+C1x+C2x2+C3x3++Cnxn. (1+x)^n = C_0 + C_1 x + C_2 x^2+ C_3x^3 + \cdots + C_n x^n.

Find the value of C02+C12++Cn2C_{0}^{2} + C_{1}^{2} + \cdots + C_{n}^{2} in terms of nn.

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