Question

Find the value of nc0 - nc1 + nc2 - nc3 +.................+(-1)^n ncn

Answer 1

the answer is zero by solving

Answer 2

$^{n}C_0 -^nC_1 +^nC_2-.........+(-1)^n \ ^nC_n=0$

Step-by-step explanation:

We know that,

$(1-x)^n=^{n}C_0 +^nC_1 (-x)^1+^nC_2(-x)^2+.........+^nC_n(-x)^n$

Now putting x=1 both sides

$(1-1)^n=^{n}C_0 +^nC_1 (-1)^1+^nC_2(-1)^2+.........+^nC_n(-1)^n$

$\Rightarrow (1-1)^n=^{n}C_0 -^nC_1 +^nC_2-.........+(-1)^n \ ^nC_n$

$\Rightarrow ^{n}C_0 -^nC_1 +^nC_2-.........+(-1)^n \ ^nC_n=0$