18.1+2+3+...+n<(1)/(8)(2n+1)^(2)

The arithmetic mean of the numbers 1, 2, 3, ...., n is

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

Mean of 1, 2, 3,...., n is .........

lim_ (n rarr oo) (1 + 2 + 3 + ... + n) / (n ^ (2) +10)

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

If 1+2 +3 + ….. + n = k then 1^(3) + 2^(3) + ….. + n^(3) is equal to……….

If S_n=1/1^3 +(1+2)/(1^3+2^3)+...+(1+2+3+...+n)/(1^3+2^3+3^3+...+n^3) Then S_n is not greater than

If =(1)/(1^(3))+(1+2)/(1^(3)+2^(3))+...+(1+2+3+...+n)/(1^(3)+2^(3)+3^(3)+...+n^(3)) Then S_(n) is not greater than

lim_ (n rarr oo) [(1 * n + 2 (n-1) + ... + n * 1) / (1 ^ (3) + 2 ^ (3) + ... + n ^ (3) ) +1] ^ (n)

The arithmetic mean of 1, 2, 3, ……., n is___