Prove that:` .^2C_1+^3C_1+^4C_1=^5C_3-1`

Prove that: 1+^3C_1+^4C_2=^5C_3

Prove that: .^(2)C_(2)+^(3)C_(2)+^(4)C_(2)+…..+^(n+1)C_(2)=1/6n(n+1)(n+2)

Prove that: .^(2)C_(2)+^(3)C_(2)+^(4)C_(2)+…..+^(n+1)C_(2)=1/6n(n+1)(n+2)

Prove that C_0 + 2.C_1 + 4.C_2 + 8.C_3 + ……+2^n.C_n = 3^n

Prove that ^m C_1^n C_m-^m C_2^(2n)C_m+^m C_3^(3n)C_m-=(-1)^(m-1)n^mdot

Prove that C_0.C_3 + C_1.C_4 + C_2.C_5 + …..+C_(n-3).C_n = ""^(2n)C_(n +3)

Prove that ^n C_1(^n C_2)(^n C_3)^3(^n C_n)^nlt=((2^n)/(n+1))^(n+1_C()_2),AAn in Ndot

Prove that (C_0+C_1)(C_1+C_2)(C_2+C_3)(C_3+C_4)...........(C_(n-1)+C_n) = (C_0C_1C_2.....C_(n-1)(n+1)^n)/(n!)

(1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + C_(3) x^(3) + … + C_(n) x^(n) , prove that C_(0) - 2C_(1) + 3C_(2) - 4C_(3) + … + (-1)^(n) (n+1) C_(n) = 0

Prove that (.^(n)C_(1))/(2) + (.^(n)C_(3))/(4) + (.^(n)C_(5))/(6) + "…." = (2^(n) - 1)/(n+1) .