1.NounAny infinite series whose terms are in geometric progression; any series of the form
a
+
a
r
+
a
r
2
+
a
r
3
⋯
=
a
∑
i
=
0
∞
r
i
{\displaystyle \textstyle a+ar+ar^{2}+ar^{3}\cdots =a\sum _{i=0}^{\infty }r^{i}}
, where
a
≠
0
{\displaystyle a\neq 0}
,
r
≠
0
{\displaystyle r\neq 0}
, and
r
≠
1
{\displaystyle r\neq 1}
.