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

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

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

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

lim_(n to oo){(1^(m)+2^(m)+3^(m)+...+ n^(m))/(n^(m+1))} equals

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

lim_( equals )(n rarr oo){(1^(m)+2^(m)+3^(m)+...+n^(m))/(n^(m+1))}

lim_(n rarr oo) {(1^(m)+2^(m)+3^(m)+…….+n^(m))/(n^(m+1))} equals

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

{:(" "Lt),(n rarr oo):} ((1^(m)+2^(m)+3^(m)+.........+n^(m))/(n^(m+1)))=

Statement-1: 1^(3)+3^(3)+5^(3)+7^(3)+...+(2n-1)^(3)ltn^(4),n in N Statement-2: If a_(1),a_(2),a_(3),…,a_(n) are n distinct positive real numbers and mgt1 , then (a_(1)^(m)+a_(2)^(m)+...+a_(n)^(m))/(n)gt((a_(1)+a_(2)+...+a_(b))/(n))^(m)