If `a=sum_(n=0)^(oo)x^n,b=sum_(n=0)^(oo)y^n,c=sum_(n=0)^(oo)(xy)^n` where `|x|,|y|<1` then

If x=sum_(n=0)^(oo) a^(n),y=sum_(n=0)^(oo)b^(n),z=sum_(n=0)^(oo)(ab)^(n) , where a,blt1 , then

If x=sum_(n=0)^(oo) a^(n),y=sum_(n=0)^(oo)b^(n),z=sum_(n=0)^(oo)(ab)^(n) , where a,blt1 , then

If x= sum_(n=0)^(oo) a^n, y=sum_(n=0)^(oo) b^n, z= sum_(n=0)^(oo) c^n , where a ,b, c are in A.P. and |a|<1, |b| <1, |c|<1, then x,y,z are in :

If quad sum_(n=0)^(oo)a^(n),y=sum_(n=0)^(oo)b^(n),z=sum_(n=0)^(oo)c^(n), wherer a,b, and c are in A.P.and |a|<,|b|<1, and |c|<1, then prove that x,y and z are in H.P.

If x = sum_(n=0)^(oo) a^(n), y=sum_(n=0)^(oo) b^(n), z = sum_(n=0)^(oo) C^(n) where a,b,c are in A.P. and |a| lt 1, |b| lt 1, |c| lt 1 , then x,y,z are in

If x = sum_(n=0)^(oo) a^(n) .,y=sum_(n=0)^(oo) b^(n) , z = sum_(n=0)^(oo) (ab)^(n) , where a,blt 1 , then :

If x=sum_(n=0)^oo a^n, y=sum_(n=0)^oo b^n, z=sum_(n=0)^oo c^n where a,b,c are in A.P and |a|<1, |b<1, |c|<1, then x,y,z are in

If s= sum_(n=0)^(oo) a^(n) , y = sum_(n=0)^(oo) b^(n) , z= sum _(n=0)^(oo) c^(n) , where a, b c are in A.P. and |a| lt 1, |b|lt 1 , |c| lt 1 then x,y,z are in :

If x=Sigma_(n=0)^(oo) a^n,y=Sigma_(n=0)^(oo) b^n,z=Sigma_(n=0)^(oo) c^n where a, b,and c are in A.P and |a|lt 1 ,|b|lt 1 and |c|1 then prove that x,y and z are in H.P