\( x=\sum_{n=0}^{\infty} a^{n}, y=\sum_{n=0}^{\infty} b^{n}, z=\sum...

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\( x=\sum_{n=0}^{\infty} a^{n}, y=\sum_{n=0}^{\infty} b^{n}, z=\sum_{n=0}^{\infty} c^{n} \), where \( a, b, c \) are in
\( \mathrm{P} \)
A.P. and \( |a|1,|b|1,|c|1, a b c \neq 0 \), then
W
(1) \( x, y, z \) are in A.P.
(2) \( x, y, z \) are in G.P.
(3) \( \frac{1}{x}, \frac{1}{y}, \frac{1}{z} \) are in A.P.
(4) \( \frac{1}{x}+\frac{1}{y}+\frac{1}{z}=1-(a+b+c) \)
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