Properties binomial coefficients

(i) the sum of binomial coefficients in the expansion of (1+x)ⁿ is 2ⁿ

(ii) the sum of odd binomial coefficients in the expansion of (1+x)ⁿ is equal to the sum of the coefficients of even terms and each is equal to 2^n-1.

iii) In the expansion of (1+x)ⁿ the coefficients of terms equidistant from the beginning and the end are equal.

(iv) C₀ – C₁ +C₂-C₃ +C₄-…+(-1) ⁿC_n = 0