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2011 Argentina National Olympiad
1
S_1+S_1^2+S_2^2+\cdots +S_{2011}^2 if S_k = sum 1/i
S_1+S_1^2+S_2^2+\cdots +S_{2011}^2 if S_k = sum 1/i
Source: 2011 Argentina OMA Finals L3 p1
January 15, 2023
algebra
Sum
Problem Statement
For
k
=
1
,
2
,
…
,
2011
k=1,2,\ldots ,2011
k
=
1
,
2
,
…
,
2011
we denote
S
k
=
1
k
+
1
k
+
1
+
⋯
+
1
2011
S_k=\frac{1}{k}+\frac{1}{k+1}+\cdots +\frac{1}{2011}
S
k
=
k
1
+
k
+
1
1
+
⋯
+
2011
1
. Compute the sum
S
1
+
S
1
2
+
S
2
2
+
⋯
+
S
2011
2
S_1+S_1^2+S_2^2+\cdots +S_{2011}^2
S
1
+
S
1
2
+
S
2
2
+
⋯
+
S
2011
2
.
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