Show that : `(1 xx 2^2+2 xx 3^2+. .+n xx(n+1)^2)/(1^2 xx 2+2^2 xx 3+. .+n^2 (n+1)) =(3 n+5)/(3 n+1)` .

Show that (1xx2^2+2xx3^2+....+nxx(n+1)^2)/(1^2xx2+2^2xx3+...+n^2xx(n+1))=(3n+5)/(3n+1) .

Find the value of (3^n × 3^(2n + 1))/(3^(2n) × 3^(n - 1))

If (1)/(2 xx 4) + (1)/(4 xx 6) + (1)/(6 xx 8) + …… n terms = (kn)/(n +1) then k is equal to

If (1 + x)^(n) = C_(0) + C_(1) x + C_(2) x^(2) + … + C_(n) x^(n) , Show that (2^(2))/(1*2) C_(0) + (2^(3))/(2*3) C_(1) + (2^(4))/(3*4)C_(2) + ...+ (2^(n+2)C_n)/((n+1)(n+2))= (3^(n+2))/((n+1)(n+2))

Give that : C_1+2C_2 x+3C_3 x^2+.....+2n. C_(2n). x^(2n-1)=2n(1+x)^(2n-1) , where C_r=((2n)!)/(r !(2n-r)!) , r=0,1,2, ,2n , then prove that C_1^2-2C_2^2+3C_3^2-..........-2n C_(2n)^2=(-1)^n . nC_n .

Prove that : ^(2n)C_n = (2^n [1.3.5. ..........(2n-1)])/(n!) .

Simplify: (2^-1xx2)/(2^2xx3^-4)^(7/2) xx (2^-2xx3^2)/(2^3xx3^-5)^(-5/2)

Using appropriate properties find : (2)/(5) xx ((-3)/(7)) - (1)/(6) xx (3)/(2) + (1)/(14) xx (2)/(5) = (2)/(5) xx ((-3)/(7)) + (1)/(14) xx (2)/(5) - (1)/(cancel6) xx (cancel 3)/(2) = (2)/(5) xx ((-3)/(7) + (1)/(14) ) - (1)/(4) = (2)/(5) xx ((-6+1)/(14))- (1)/(4) = (cancel 2)/(cancel 5) xx (-cancel 5)/(cancel14) - (1)/(4) = (-1)/(7) - (1)/(4) (- 4 - 7)/(28) = (-11)/(28)

Let A and B be two sets such that n(A) = 3 and n(B) = 2. If (x, 1), (y, 2),(z, 1) are in A xx B , find A and B. where x, y and z are distinct elements.