Prove that : $C_{0} + C_{1} + C_{2} + . . . . . . + C_{n} = 2^{n}$ ?

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Solution

cornder $(1 + x)^{n} =^{n} C_{0} +^{n} C_{1} x^{1} +^{n} C_{2} x^{2} + . . .$
put x = 1
$\Rightarrow 2^{n} =^{n} C_{0} +^{n} C_{1} +^{n} C_{2} + . . .$

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