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Mathematics
Problem
Let
S
n
=
a
+
a
r
+
a
r
2
+
⋯
+
a
r
n
−
1
S_n = a + ar + ar^2 + \dots + ar^{n-1}
S
n
=
a
+
a
r
+
a
r
2
+
⋯
+
a
r
n
−
1
with
r
≠
1
r \neq 1
r
=
1
. After multiplying by
r
r
r
and subtracting, what is
S
n
−
r
S
n
S_n - rS_n
S
n
−
r
S
n
equal to? a)
a
(
r
n
−
1
)
a(r^{n}-1)
a
(
r
n
−
1
)
b)
a
(
1
−
r
n
−
1
)
a(1-r^{n-1})
a
(
1
−
r
n
−
1
)
c)
a
(
1
−
r
n
)
a(1-r^{n})
a
(
1
−
r
n
)
d)
a
r
(
1
−
r
n
−
1
)
ar(1-r^{n-1})
a
r
(
1
−
r
n
−
1
)
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