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# The value of $^nC_0-^nC_1$ + $^nC_2-......$ + $(-1)^n$ $^n C_n$ = ?

$\begin{array}{1 1} 2^n \\ 2^n-1 \\ 2^{n-1} \\ 0 \end{array}$

$(1-x)^n=^nC_0-^nC_1x+............(-1)^n$$^nC_n x^n Put x=1 0=^nC_0-^nC_1+.............(-1)^n$$^nC_n$
Hence the value is 0
edited Aug 8, 2014