Verify that C(2,1) + C(3,1) + C(4,1) = C(3,2) + C(4,2)

Verify that 2 C (7,4)= C(8,4) .

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + C_(3)x^(3) + ...+ C_(n)x^(n) , prove that (C_(1))/(2) + (C_(3))/(4) + (C_(5))/(6) + …= (2^(n)-1)/(n+1) .

If (1 + x)^(n) = C_(0) + C_(1)x + C_(2)x^(2) + C_(3) x^(3) + C_(4) x^(4) + ..., find the values of (i) C_(0) - C_(2) + C_(4) - C_(6) + … (ii) C_(1) - C_(3) + C_(5) - C_(7) + … (iii) C_(0) + C_(3) + C_(6) + …

Let A= {1, 2}, B = {1, 2, 3, 4}, C = {5, 6} andD = {5, 6, 7, 8}. Verify that A xx (B nn C) = (A xx B) nn (A xx C) .

Show that (C_(0))/(1) - (C_(1))/(4) + (C_(2))/(7) - … + (-1)^(n) (C_(n))/(3n +1) = (3^(n) * n!)/(1*4*7…(3n+1)) , where C_(r) stands for ""^(n)C_(r) .

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + …+ C_(n) x^(n) , prove that (1*2) C_(2) + (2*3) C_(3) + …+ {(n-1)*n} C_(n) = n(n-1) 2^(n-2) .

Verify that : "^8C_4+ ^8C_3= ^9C_4 .

If A= {1, 2, 3}, B= {4},C = {5}. then verify that : A xx (B nn C)= (A xxB) nn (A xx C) .

If A= {1, 2, 3}, B= {4},C = {5}. then verify that : A xx (B - C)= (A xxB) - (A xx C) .