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If x=(1)/(1^(2))+(1)/(3^(2))+(1)/(5^(2))...

If `x=(1)/(1^(2))+(1)/(3^(2))+(1)/(5^(2))+....` , `y=(1)/(1^(2))+(3)/(2^(2))+(1)/(3^(2))+(3)/(4^(2))+....` and `z=(1)/(1^(2))-(1)/(2^(2))+(1)/(3^(2))-(1)/(4^(2))+...` then

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If x=(1)/(1^(2))+(1)/(3^(2))+(1)/(5^(2))+ . . . y=(1)/(1^(2))+(3)/(2^(2))+(1)/(3^(2))+(3)/(4^(2))+ . . . . z=(1)/(1^(2))-(1)/(2^(2))+(1)/(3^(2))-(1)/(4^(2))+ . . .then

((1)/(2)x^(2)-(1)/(2)y^(2)+(1)/(4)z^(2))-((1)/(3)x^2+(1)/(4)y^(2)+(1)/(2)z^(2))+((1)/(4)x^(2)+(1)/(3)y^(2)+(1)/(3)z^(2))

(1)/(1.3).(1)/(2)+(1)/(2.4).(1)/(2^(2))+(1)/(3.5).(1)/(2^(3))+....=

(x+1)/(3)=(y+2)/(1)=(z+1)/(2) and (x-2)/(1)=(y+2)/(2)=(z-3)/(3)

Solve : (1)/(2x)+(1)/(4y)-(1)/(3z)=(1)/(4),(1)/(x)=(1)/(3y),(1)/(x)-(1)/(5y)+(4)/(z)=2 (2)/(15)

Find the S.D. between the lines : (i) (x)/(2) = (y)/(-3) = (z)/(1) and (x -2)/(3) = (y - 1)/(-5) = (z + 4)/(2) (ii) (x -1)/(2) = (y - 2)/(3) = (z - 3)/(2) and (x + 1)/(3) = (y - 1)/(2) = (z - 1)/(5) (iii) (x + 1)/(7) = (y + 1)/(-6) = (z + 1)/(1) and (x -3)/(1) = (y -5)/(-2) = (z - 7)/(1) (iv) (x - 3)/(3) = (y - 8)/(-1) = (z-3)/(1) and (x + 3)/(-3) = (y +7)/(2) = (z -6)/(4) .