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8
2016 Algebra #8
2016 Algebra #8
Source:
August 6, 2022
2016
Algebra Test
Problem Statement
It is possible to express the sum
∑
n
=
1
24
1
n
+
n
2
−
1
\sum_{n=1}^{24}\frac{1}{\sqrt{n+\sqrt{n^2-1}}}
n
=
1
∑
24
n
+
n
2
−
1
1
as
a
2
+
b
3
a\sqrt{2}+b\sqrt{3}
a
2
+
b
3
, for some integers
a
a
a
and
b
b
b
. Compute the ordered pair
(
a
,
b
)
(a,b)
(
a
,
b
)
.
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