(1)/(1^(3))+(1+2)/(1^(3)+2^(3))+(1+2+3)/(1^(3)+2^(3)+3^(3))

The sum of (1^(3))/(1)+(1^(3)+2^(3))/(1+2)+ (1^(3)+2^(3)+3^(3))/(1+2+3)+.. . upto 10 terms is

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

((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

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))/(1^(3))+(2^(2))/(2^(3))+(1^(2)+2^(2)+3^(2))/(1^(3)+2^(3)+3^(3))+ . . . , is

value of 1+(1^(3)+2^(3))/(1+2)+(1^(3)+2^(3)+3^(3))/(1+2+3)+……+ (1^(3)+2^(3)+….15^(3))/(1+2+…+15)-(1)/(2)(1+2+….+15) is

((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

(((1)/(2))*((2)/(2)))/(1^(3))+(((2)/(2))*((3)/(2)))/(1^(3)+2^(3))+(((3)/(2))*((4)/(2)))/(1^(3)+2^(3)+3^(3))+...=

value of 1+(1^(3)+2^(3))/(1+2)+(1^(3)+2^(3)+3^(3))/(1+2+3)+......+(1^(3)+2^(3)+....15^(3))/(1+2+...+15)-(1)/(2)(1+2+...+15)

The direction cosines of the vector 2hati+2hatj-hatk are: a) (2)/(3),(1)/(3),(1)/(3) b) (1)/(3),(1)/(3),(2)/(3) c) (1)/(3),(-2)/(3),(2)/(3) d) (2)/(3),(2)/(3),(-1)/(3)