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1998 ITAMO
1
sum_{n=1}^{1.000.000}[ \sqrt{n} ]
sum_{n=1}^{1.000.000}[ \sqrt{n} ]
Source: ITAMO 1998 p1
January 25, 2020
Sum
algebra
radical
Problem Statement
Calculate the sum
∑
n
=
1
1.000.000
[
n
]
\sum_{n=1}^{1.000.000}[ \sqrt{n} ]
∑
n
=
1
1.000.000
[
n
]
. You may use the formula
∑
i
=
1
k
i
2
=
k
(
k
+
1
)
(
2
k
+
1
)
6
\sum_{i=1}^{k} i^2=\frac{k(k +1)(2k +1)}{6}
∑
i
=
1
k
i
2
=
6
k
(
k
+
1
)
(
2
k
+
1
)
without a proof.
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