MathDB
Problems
Contests
National and Regional Contests
India Contests
Assam Mathematics Olympiad
2023 Assam Mathematics Olympiad
13
13
Part of
2023 Assam Mathematics Olympiad
Problems
(1)
Assam Mathematics Olympiad 2023 Category III Q13
Source:
9/11/2024
Let
S
(
r
)
S(r)
S
(
r
)
denote the sum of the infinite geometric series
17
+
17
r
+
17
r
2
+
17
r
3
+
.
.
.
17 + 17r + 17r^2 +17r^3 + . . .
17
+
17
r
+
17
r
2
+
17
r
3
+
...
for
−
1
<
r
<
1
-1 < r < 1
−
1
<
r
<
1
. If
S
(
a
)
×
S
(
−
a
)
=
2023
S(a) \times S(-a) = 2023
S
(
a
)
×
S
(
−
a
)
=
2023
, find
S
(
a
)
+
S
(
−
a
)
S(a) + S(-a)
S
(
a
)
+
S
(
−
a
)
.