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)^mdot`

If mgt1 and ninN , such that 1^(m)+2^(m)+3^(m)+...+n^(m)gtn((n+1)/(k))^(m) Then, k=

If m is negative or positive and greater than 1 , show that 1^(m)+3^(m)+5^(m)+….+(2n-1)^(m) gt n^(m+1)

If a^m .a^n = a^(mn) , then m(n - 2) + n(m- 2) is :

lim_(x->0) [(2^m +x)^(1/m)-(2^m+x)^(1/n)]/x a) 1/(m2^m)-1/(n2^n) b) 1/(m2^(m-1))-1/(n2^(n-1)) c) m/2^(m-1)-n/2^(n-1) d) none of these

Prove that mC_(1)^(n)C_(m)-^(m)C_(2)^(2n)C_(m)+^(m)C_(3)^(3n)C_(m)-...=(-1)^(m-1)n^(m)

For any non-zero integers 'a' and 'b" and whole numbers m and n. - a^(m) xx a^(n) = a^(m+n) a^(m) =a^(n), a gt 0 rArr m=n a^(m) + a^(n)=a^(m-n) If (2/9)^(3) xx (2/9)^(6) =(2/9)^(2m-1) , then m equals

If (m+n)/(m-n)=7/3 then (m^2-n^2)/(m^2+n^2)=

IfI_(m , n)=int_0^(pi/2)sin^m xcos^n xdx , Then show that I_(m , n)=(m-1)/(m+n)I_m-2n(m ,n in N) Hence, prove that I_(m , n)=f(x)={((n-1)(n-3)(m-5)(n-1)(n-3)(n-5))/((m+n)(m+n-2)(m+n-4))pi/4w h e nbot hma n dna r ee v e n((m-1)(m-3)(m-5)(n-1)(n-3)(n-5))/((m+n)(m+n-2)(m+n-4))