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

For all n ge 1 prove that 1^(2)+2^(2)+ 3^(2)+4^(2)+….+n^(2)= (n(n+1)(2n+1))/(6)

Prove that .^(n-1)C_(3)+.^(n-1)C_(4) gt .^(n)C_(3) if n gt 7 .

Prove that 1* ""^(1)P_(1)+2* ""^(2)P_(2)+3* ""^(3)P_(3) + … +n* ""^(n)P_(n)=""^(n+1)P_(n+1)-1

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

lim_(n to oo) ((n)/(1 + n^2) + n/(2^2 + n^2) + n/(3^2 + n^2) + ……. + n/(n^2 + n^2)) is :

The value of lim_(n rarr oo) (1 + 2^(4) + 3^(4) +…...+n^(4))/(n^(5)) - lim_(n rarr oo) (1 + 2^(3) + 3^(3) +…...+n^(3))/(n^(5)) is :

1^(2) + 1+ 2^(2) + 2 + 3^(2) + 3+"............"+n^(2) + n is equal to :

The sum 1^(2)+1+2^(2)+2+3^(2)+3+..+n^(2)+n is

If n C_(1)+2. n C_(2)+..n. n C_(n) = 2 n^(2) , then n =