If `m >1,n in N` show that `1^m+2^m+2^(2m)+2^(3m)+...+2^(n m-m)> n^(1-m)(2^n-1)^m`

Prove that ^mC_1^n C_m-^m C_2^(2n)C_m+^m C_3^(3n)C_m-.....=(-1)^(m-1)n^mdot

A function f is defined by f(x)=|x|^m|x-1|^nAAx in Rdot The local maximum value of the function is (m ,n in N) (a) 1 (b) m^n.n^m (c) (m^m n^n)/((m+n)^(m+n)) (d) ((m n)^(m n))/((m+n)^(m+n))

If m=.^(n)C_(2) show that , .^(m)C_(2)=3.^(n+1)C_(4)

m^(3)-n^(3)-m(m^(2)-n^(2))+n(m-n)^(2)

Factorise : 2(m^(2)+n^(2))^(2)-3mn(m^(2)+n^(2))-2m^(2)n^(2)

Using formula let's show that. (3m + 4n)^2 = (3m - 4n)^2 + 48mn

A is a set containing n elements. A subset P_1 is chosen and A is reconstructed by replacing the elements of P_1 . The same process is repeated for subsets P_1,P_2,....,P_m with m>1 . The number of ways of choosing P_1,P_2,....,P_m so that P_1 cup P_2 cup....cup P_m=A is (a) (2^m-1)^(mn) (b) (2^n-1)^m (c) (m+n)C_m (d) none of these

Evaluate: lim_(nrarroo)(1^(m)+2^(m)+3^(m)+...+n^(m))/(n^(m+1))(mgt-1)

The ratio of the sums of m and n terms of an A.P. is m^2 : n^2. Show that the ratio of m^(th) and n^(th) term is (2m-1) : (2n -1) .

If m, n in R , then the value of I(m,n)=int_(0)^(1) t^(m)(1+t)^(n)dt is -