8.1+2+3+...+n<(1)/(8)(2n+1)^(2)

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

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))

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

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

nth term of 1+(1+2)+(1+2+3)+..............(1+2+3+...+n) is

Sum up 1 + (1+2)+(1+ 2+3) +...+(1+2+3+...+ n ) .

lim_ (n rarr oo) ((1) / (2) +1+ (3) / (2) + ... + (n) / (2)) / (25n ^ (2) + n + 3)

Let S_(n) = ( 1)/( 1^(3)) + ( 1+2)/( 1^(3) + 2^(3)) +"...." + ( 1+ 2 + "...." + n)/(1^(3) +2^(3)"...."+n^(3)), n = 1,2,3,"....." , Then S_(n) is not greater than :

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