We have (1+xn) = C0+C1x+C2x2 + ... + Cnxn ... (1) (1−
1
x
)n = C0 -
C1
x
+
C2
x2
+ ... + (−1)n
Cn
xn
... (2) ∴ C02−C12+C22 ... + (−1)nCn2 = co-eff. Of the term independent of x in Product of R.H.S. (1)and (2) = co-eff. Of term independent of x in (1+x)n(1−