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2018 PUMaC Algebra A
1
1
Part of
2018 PUMaC Algebra A
Problems
(1)
2018 PUMaC Algebra A1
Source:
11/25/2018
Let
a
k
=
0.
0
…
0
⏞
k
−
1
0
′
s
1
0
…
0
⏞
k
−
1
0
′
s
1
a_k = 0.\overbrace{0 \ldots 0}^{k - 1 \: 0's} 1 \overbrace{0 \ldots 0}^{k - 1 \: 0's} 1
a
k
=
0.
0
…
0
k
−
1
0
′
s
1
0
…
0
k
−
1
0
′
s
1
The value of
∑
k
=
1
∞
a
k
\sum_{k = 1}^\infty a_k
∑
k
=
1
∞
a
k
can be expressed as a rational number
p
q
\frac{p}{q}
q
p
in simplest form. Find
p
+
q
p + q
p
+
q
.
algebra