Find the value of nC0 - nC1 + nC2 - nC3 +.................+(-1)^n nCn

Expand (1+x)^n = (nC0) + (nC1) x +(nC2) x^2 + (nC3)x^3 +...(nCn)x^n 
Put x = -1 in both sides 

(1-1)^n = (nC0)-(nC1)+(nC2)-(nC3)+...+ (nCn)(-1)^n 

so, (nC0)-(nC1)+(nC2)-(nC3)+...+(nCn)(-1)^n = 0 

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General expansion for (a-b)2

nC0a0bn +nCa1bn-1 -nCa2bn-2 +..........+nCanbn-n

Since a and b in the above question are missing they have to have a value of 1 i.e. a=1, b=1

GE for above question: (1 - 1)n = 0n = 0

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