1^(2)+2^(2)+...+n^(2)>(n^(3))/(3),n in N

Prove that 1^(2) +2^(2)+ ….+n^(2) gt (n^(3))/(3) n in N

Prove that 1^(2) +2^(2)+ ….+n^(2) gt (n^(3))/(3) , n in N

Prove that: 1^2+2^2+3^2.....+n^2>(n^3)/3, n in N

Prove that, 1^2 + 2^2 + …..+ n^2 gt (n^3)/(3) , n in N

lim_(n rarr oo) (1^(2)+2^(2)+....+n^(2))/(2n^(3)+3n^(2)+4n+1 ) =

Prove that 1^2+2^2+dotdotdot+n^2>(n^3)/3, n in N

1^(3)+2^(3)+3^(3)+.....+n^(3)=(n(n+1)^(2))/(4), n in N

Match the following . {:(,"ColumnI",,"ColumnII"),((i) ,1^(2) +2^(2) +3^(2) +....+n^(2) ,(a) ,[(n(n+1))/(2)]^(2)),((ii) , 1^(3) +2^(2) +3^(2) +...+n^(3) ,(b), n(n+1)),((iii),2+4+6+...+2n,( c),(n(n+1)(2n+1))/(6)),((iv),1+2+3+...+n,(d),(n(n+1))/(2)):}

f(n)=(1^(2)n+2^(2)(n-1)+3^(2)(n-2)+...+n^(21))/(1^(3)+2^(3)+3^(3)+......+n^(3)) then (where [.] denotes greatest integer function)