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Q. The arithmetic mean of the series $n_{c_{0}}, n_{c_{1}}, n_{c_{2}} \ldots . n_{c_{n}}$ is

Solution:

$A . M=\frac{n_{c_{0}}+n_{c_{1}}+n_{c_{2}}+\ldots . .+n_{c_{n}}}{n+1}=\frac{2^{n}}{n+1}$