If `x=a+a/r+a/(r^2)+oo,y=b-b/r+b/(r^2)+oo,a n dz=c+c/(r^2)+c/(r^4)+oo,` prove that `(x y)/z=(a b)/cdot`

If x=a+(a)/(r)+(a)/(r^(2))+...oo,y=b-(b)/(r)+(b)/(r^(2))+...oo, and z=c+(c)/(r^(2))+(c)/(r^(4))+...oo prove that (xy)/(z)=(ab)/(c)

"If "x=a+(a)/(r)+(a)/(r^(2))+...oo,y=b-(b)/(r)+(b)/(r^(2))-...oo,"and "z=c+(c)/(r^(2))+(c)/(r^(4))+...oo," then prove that "(xy)/(z)=(ab)/(c).

if r>1 and x=a+(a)/(r)+(a)/(r^(2))+.........oo,y=b-(b)/(r)+(b)/(r^(2))-(b)/(r^(2)) and z=c+(c)/(r^(2))+(c)/(r^(4))+............oo then (xy)/(z)

If A=1+r^(a)+r^(2a)+ to oo andB=1+r^(b)+r^(2b)+oo, prove that r=((A-1)/(A))^(1/a)=((B-1)/(B))^(1/b)

If r>1 and x=a+(a)/(r)+(a)/(r^(2))............,y=b+(b)/(r)+(b)/(r^(2))...... and z=b+(b)/(r)+(b)/(r^(2))+.......... Then value of (xy)/(z^(2)) is

If x=r sin A cos C,quad y=r sin A sin C and z=r cos A, prove that r^(2)=x^(2)+y^(2)+z^(2)

If a = sum_(r=1)^(oo) 1/(r^(2)), b = sum_(r=1)^(oo) 1/((2r-1)^(2)), then (3a)/b is equal to _____

If A=1+r^(2)+r^(2a)+...oo=a and B=1+r^(b)+r^(2b)+...oo=b then (a)/(b) is equal to

If a=sum_(n=r)^( oo)(1)/(r^(4)) then sum_(r=1)^(oo)(1)/((2r-1)^(4))=