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Sweden Contests
Swedish Mathematical Competition
1983 Swedish Mathematical Competition
1
1
Part of
1983 Swedish Mathematical Competition
Problems
(1)
n-th sum if pos. integers are grouped as 1, 2+3, 4+5+6, 7+8+9+10,...
Source: 1983 Swedish Mathematical Competition p1
3/28/2021
The positive integers are grouped as follows:
1
,
2
+
3
,
4
+
5
+
6
,
7
+
8
+
9
+
10
,
…
1, 2+3, 4+5+6, 7+8+9+10,\dots
1
,
2
+
3
,
4
+
5
+
6
,
7
+
8
+
9
+
10
,
…
. Find the value of the
n
n
n
-th sum.
Sum
algebra