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1300
Telescoping Reciprocals
Editorial
algebra
sequences
telescoping
A sequence is defined by
a
1
=
2
a_1 = 2
a
1
=
2
and the recursive formula
a
n
+
1
=
a
n
+
2
n
+
2
a_{n+1} = a_n + 2n + 2
a
n
+
1
=
a
n
+
2
n
+
2
for all integers
n
≥
1
n \ge 1
n
≥
1
. If the value of the sum
∑
k
=
1
10
1
a
k
\sum_{k=1}^{10} \frac{1}{a_k}
k
=
1
∑
10
a
k
1
is expressed as a fraction in simplest form
p
q
\frac{p}{q}
q
p
, what is the value of
p
+
q
p + q
p
+
q
?
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