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

Step-by-step solution

array ll x= _ n=0 ^ a^n= 1 1-a & a=1- 1 x y= _ n=0 ^ b^n= 1 1-b & b=1- 1 y array aligned & z= _ n=0 ^ c^n= 1 1-c c=1- 1 z & a, b, c are in A.P. & 2 b=a+c & 2 (1- 1 y )=1- 1 x +1- 1 y & 2 y = 1 x + 1 z & x, y, z are in H.P. aligned