" I) "S_(n)=1+(1+2)/(1^(3)+2^(3))+(1+2+3)/(1^(3)+2^(3)+3^(3))+...." n terms "

If (1)/(1^(3))+(1+2)/(1^(3)+2^(3))+(1+2+3)/(1^(3)+2^(3)+3^(3))+......n terms then lim_(n rarr oo)[S_(n)]

If the sum of n terms of the series : (1)/( 1^(3)) +( 1+2)/( 1^(3) + 2^(3)) +(1+2+3)/(1^(3) + 2^(3) + 3^(3)) + "......." in S_(n) , then S_(n) exceeds 199 for all n greater than :

((1)/(2) . (2)/(2))/(1^(3))+((2)/(3) . (3)/(2))/(1^(3)+2^(3)) +((3)/(2) . (4)/(2))/(1^(3)+2^(3)+3^(3))+.. . . to n terms

((1)/(2), (2)/(2) )/(1^3) + ((2)/(2) , (3)/(2) )/( 1^3 + 2^3) + ((3)/(2) , (4)/(2) ) / (1^(3) + 2^(3) + 3^(3) ) + ..... n terms

S_(n)=(1)/(1^(3))+(1+2)/(1^(3)+2^(3))+(1+2+3)/(1^(3)+2^(3)+3^(3))+......+(1+2+....+n)/(1^(3)+2^(3)+......+n^(3)).100S_(n)=n then n is equal to :

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

Let H_(n)=1+(1)/(2)+(1)/(3)+ . . . . .+(1)/(n) , then the sum to n terms of the series (1^(2))/(1^(3))+(1^(2)+2^(2))/(1^(3)+2^(3))+(1^(2)+2^(2)+3^(2))/(1^(3)+2^(3)+3^(3))+ . . . , is

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 :

If 1/1^3 + (1+2)/(1^3+2^3)+(1+2+3)/(1^3+2^3+3^3) +.......n terms then lim_(n->oo) [S_n]

1^(3) + 1^(2) + 1+2^(3) + 2^(2) + 2+3^(2) + 3^(2) + 3+3… 3n terms =