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2
2000 Guts #2: Infinite geometric series
2000 Guts #2: Infinite geometric series
Source:
October 12, 2014
geometric series
Problem Statement
If
X
=
1
+
x
+
x
2
+
x
3
+
⋯
X=1+x+x^2+x^3+\cdots
X
=
1
+
x
+
x
2
+
x
3
+
⋯
and
Y
=
1
+
y
+
y
2
+
y
3
+
⋯
Y=1+y+y^2+y^3+\cdots
Y
=
1
+
y
+
y
2
+
y
3
+
⋯
, what is
1
+
x
y
+
x
2
y
2
+
x
3
y
3
+
⋯
1+xy+x^2y^2+x^3y^3+\cdots
1
+
x
y
+
x
2
y
2
+
x
3
y
3
+
⋯
in terms of
X
X
X
and
Y
Y
Y
only?
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