If \( x = \displaystyle \sum_{n=0}^{\infty} a^n \), \( y = \displaystyle \sum_{n=0}^{\infty} b^n \), \( z = \displaystyle \sum_{n=0}^{\infty} c^n \), where \( a, b, c \) are in A.P. and \( |a| < 1 \), \( |b| < 1 \), \( |c| < 1 \), \( abc \neq 0 \), then:
