`(2)/(3)+(1)/(2)((2)/(3))^(2)+(1)/(3)((2)/(3))^(3)+....=`

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)

(2)/(3) -((1)/(2) -(1)/(3))/((1)/(2)+(1)/(3))xx3(1)/(3)+(5)/(6) =?

Simplify ((3(2)/(3))^(2)-(2 (1)/(2)))/((4(3)/(4))^(2)-(3(1)/(3))^(2))+(3(2)/(3)-2(1)/(2))/(4(3)/(4)-3(1)/(3))

((3(2)/(3))^(2)-(2(1)/(2))^(2))/((4(3)/(4))^(2)-(3(1)/(3))^(2))-:(3(2)/(3)-2(1)/(2))/(4(3)/(4)-3(1)/(3))=?(37)/(97) (b) (74)/(97)( c) 1(23)/(74) (d) None of these

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

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

((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

Find the sum: (1)/(3) + (2)/(3^(2)) + (1)/(3^(3)) + (2)/(3^(4)) + (1)/(3^(5)) + (2)/(3^(6)) + …..oo

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